The perimeter of a triangle is 84 meters. The longest side of the triangle is 7 meters less than twice the length of the shortest side ,x. The middle side is 7 meters longer than the shortest side. What is the length of each side of the triangle.

Answers

Answer 1

Hey ! there

Answer:

Smallest side = 21 m

Middle side = 28 m

Longest side = 35 m

Step-by-step explanation:

In this question we are given that perimeter of a triangle is 84 m , longest side of triangle is 7 meters less than twice the length of shortest side that is x and middle side is 7 meters longer than the shortest side .

And we're asked to find the length of each side of triangle.

So ,

Shortest side = x m

Middle side = ( x + 7 ) m ( Because in question it is given that middle side is 7 metres longer than the shorter side )

Longest side = ( 2x -7 ) m ( Because in question it is given that longest side is 7 m less than twice the length of shortest side )

We know that ,

[tex]\underline{\boxed{\frak{Perimeter_{(Triangle)} = Sum \:of\: three\: sides}}}[/tex]

Solution : -

[tex] \longmapsto \qquad x +( x + 7) + (2x - 7) = 84[/tex]

Step 1 : Removing parenthesis and cancelling 7 with -7 :

[tex] \longmapsto \qquad x + x + \cancel{7} + 2x - \cancel{ 7 }= 84[/tex]

Step 2 : Adding like terms on left side :

[tex] \longmapsto \qquad 4x = 84[/tex]

Step 3 : Dividing with 4 on both sides :

[tex] \longmapsto \qquad \dfrac{ \cancel{4}x}{ \cancel{4}} = \cancel{\dfrac{ 84}{4} }[/tex]

On calculating further, We get :

[tex] \longmapsto \qquad \red{\underline{\boxed{\frak{ x = 21 \: m}}}}\quad \bigstar[/tex]

According to question ,

x = smallest side

Henceforth , smallest side of triangle is 21 meters .

▬▬▬▬▬▬▬▬▬▬▬▬▬▬

x + 7 = middle side21 + 7 = 28

Henceforth , middle side of triangle is 13 meters .

▬▬▬▬▬▬▬▬▬▬▬▬▬▬

2x - 7 = longest side2(21) - 742 - 735

Henceforth , longest side of triangle is 35 meters .

Verifying : -

Now we are checking our answer by adding all the sides and equating it with given perimeter that is 84 metres .

21 + 28 + 35 = 84

49 + 35 = 84

84 = 84

L.H.S = R.H.S

Hence , Verified .

Therefore , our answer is correct.

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Related Questions

A quadrilateral is inscribed in a circle two of the angles are 33° and 57°. Which statements are correct?

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Answer:

Step-by-step explanation:

Remark

If you are given choices, you should quote them; Otherwise we are guessing. I will give you some some choices.

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Answer:

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Solve the equation for all values of x by completing the square.
x2 + 8.0 + 15 = 0

Answers

Answer:

x= -3

x= -5

Step-by-step explanation:

x^2 + 8x + 15 = 0

find which 2 numbers when multiplied equal 15 and when added equal 8

they are 3 and 5

(x+3)(x+5)

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please help asap!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

30.96

Step-by-step explanation:

First you must find the diameter of the circle which is 12

Then you must use the formula A=πr²

So it should be = to A = 3.14 ×144 which is 30.96

[tex] \huge \tt \color{pink}{A}\color{blue}{n}\color{red}{s}\color{green}{w}\color{grey}{e}\color{purple}{r }[/tex]

[tex] \large\underline{ \boxed{ \sf{✰\:Notes }}}[/tex]

★ Concept ★➣ A square with sides 12m➣then a circle in between➣nd it's diameter is 12m bcz of side of square is equal to radius➣soo here things we to find is the area of circle and then square then by subtracting their will give us the area of shaded part in image

[tex] \rule{70mm}{2.9pt}[/tex]

[tex] \large\underline{ \boxed{ \sf{✰\: formule\: used\:✰ }}}[/tex]

[tex]{ \boxed{✟\underline{ \boxed{ \sf{\: Area \: of \: circle = \pi {r}^{2} \: }}}✟}}[/tex]

[tex]{ \boxed{✟\underline{ \boxed{ \sf{\: Area \: of \: square = side \times side \: or \: ( {s}^{2}) \: }}}✟}}[/tex]

[tex] \rule{70mm}{2.9pt}[/tex]

1st taking out the the area of circle

➣ value of pi = 3.14➣ diameter = 12m (have to find radius we know that radius is half of diameter) which is

[tex] \qquad \rm{➛ \: radius(r) = \frac{12}{2} } \\ \\ \qquad \rm{➛ \: radius(r) = \frac{ \cancel{12}}{ \cancel2} } \\ \\ \qquad \rm{➛ \: radius(r) =6m}[/tex]

★ Hence radius of circle is 6m★ let's substitute values now ★

[tex] \\ \qquad \rm{➛Area \: of \: circle = 3.14 \times {6}^{2} \:} \\ \\ \qquad \rm{➛Area \: of \: circle = \:3.14 \times 36} \\ \\ \qquad \rm{➛Area \: of \: circle = \:113.04 {m}^{2} }[/tex]

[tex] \rule{70mm}{2.9pt}[/tex]

now finding the area of square

➣ here two given side are 12m

★ let's substitute values now ★

[tex]\\ \qquad \rm{➛Area \: of \:square = 12×12} \\ \\ \\ \qquad \rm{➛Area \: of \:square = 144 {m}^{2} }[/tex]

✞ Now according to given ques we have to find area of shaded part soo let's solve ! ✞

[tex]\\ \rm{➛Area \: of \:shaded \: part = \: area \: of \: circle - area \: of \: squre} \\ [/tex]

Let's substitute value

[tex]\\ \rm{➛Area \: of \:shaded \: part =113.04-144} \\ \\ \qquad \rm{➛Area \: of \:shaded \: part =30.96 {m}^{2} }[/tex]

[tex] \rule{70mm}{2.9pt}[/tex]

★ Hence area of shaded part =

[tex]{ \boxed{✜\underline{ \boxed{ \sf{ \: 30.96 {m}^{2} \green✓\: }}}✜}}[/tex]

★ note here we neglect minus (-)

[tex] \rule{70mm}{2.9pt}[/tex]

Hope it helps !

help me pls it will help me alot

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Answer:

h > 1600

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Since the elevation at which it is difficult for Matt to breathe (h) has to be *higher* than 1600, h is greater than 1600.

Which statement is FALSE?

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i need to find the value of each variable in the following parallelograms

Answers

Answer
X=16
Y=13
Explanation
The opposites sides of a parallelogram are equal
7x-8=6x+8
7x-6x=8+8
X=16
The opposites angles of a parallelogram are equal
Then the sum of all the inside angles is equal to 360, and you have two of the inside angles
2(8y-4)+2(6y+2)=360
16y-8+12y+4=360
16y+12y=360+8-4
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Answer:

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Step-by-step explanation:

sorry for the bad handwriting lol

Andrea recorded the points she scored in her last eight basketball games:
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Answer:

You could ask what her average score is using mean (which is 36.25)

Step-by-step explanation:

Answer:

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Step-by-step explanation:

How can I solve this and plot the inequality?

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Answers

Answer:

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The net of a triangular prism is shown. Use the ruler provided to measure the dimensions of the net to the nearest half centimeter. What is the total surface area of the rectangular prism in square centimeters?

Answers

If the area of the triangle and the rectangle is 4 square cm and 2 square cm. Then the total surface area of the triangular prism will be 14 square cm.

What is a triangular prism?

A closed solid with two parallel triangular bases joined by a rectangle surface is known as a triangular prism.

The total surface area of the triangular prism will be

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The area of the rectangle will be

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Then the total surface area will be

Total surface area = 2 x 4 + 3 x 2

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Answers

Answer:

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Step-by-step explanation: I found this and it can help you!

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Answers

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How to determine the transformations of a function

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[tex]g(x) = 2^{x}+6[/tex]

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Need help with this quick. Find the measure of B and the value of z if ABC~DEF.

Answers

Z = 5

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Jamie drove to the beach. She started driving at 11:50 a.m. It took her 4 hours and 25 minutes to get to the beach.

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Answers

It is 5:15 Because you add 11 +4 =15 then you

Use each table to find the requested ratio. ITEM BANK: Move to Bottom
1:2 1:4 1:5 2:1 4:1 5:1

Answers

Answer:

See below ~

Step-by-step explanation:

Table 1

⇒ Side length : Perimeter = 1 : 4

⇒ Perimeter : Side length = 4 : 1

Table 2

⇒ Radius : Diameter = 1 : 2

⇒ Diameter : Radius = 2 : 1

Table 3

⇒ Number of people : Number of tables = 5 : 1

⇒ Number of tables : Number of people = 1 : 5

How much work is done by a man who uses a force of 7 Newtons to push a box 3 meters across the room?

Answers

Answer: 21 J (Joules) of work done.

Step-by-step explanation:

W = Fs, where F is force and s is displacement.

F = 7 N

s = 3 m

W = 7 N * 3 m = 21 N*m, or 21 J

21 N/m of work is done by a man to push the box.

What is Work done?

The displacement plus a component of the applied force of the item in the direction of displacement make up the work done by a force. Work is accomplished when we push a block with some force; the body moves more quickly.

We have,

Force = 7 Newton

Distance = 3 m

We know, Work done = Force x distance

Work done = 7 x 3

Work done = 21 N/m

Thus, the amount work done is 21 N/m.

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Which statements are true? Check all that apply. The corresponding sides of similar triangles have proportional lengths. The corresponding sides of congruent triangles have the same lengths. The corresponding angles of similar triangles have different measures. If corresponding sides of two triangles are not the same length, the triangles are not similar. If corresponding sides of two triangles are not the same length, the triangles are not congruent.

Answers

The answers to this question are A,B and E

how do i do this I forgot how to do this and I have a test tomorrow

Answers

Answer:

Step-by-step explanation:

(1 + 11)/(-2+5)= 12/3=4

y + 11 = 4(x + 5)

y + 11 = 4x + 20

y = 4x + 9

can yall help me with this?
Thank you!

Answers

Answer:

1260 degrees (1260°)

Step-by-step explanation:

Formula to Find Sum of Interior Angles of a Polygon

180 (n - 2)n is the number of sides of the polygon

Nonagon (9-sided polygon)

180 (9 - 2)180 × 71260 degrees (1260°)

How much paper is used for the label on the can of peas?

Answers

Answer:

here

Step-by-step explanation:

find the circumference of the lid (this is like a side length of a rectangle)

2*pi*2= 12.566in

Then multiply by 3 (the other side length)

12.566*3= 37.7in squared :)

23h−13h+11=8
please help me

Answers

Answer:

h = - [tex]\frac{3}{10}[/tex]

Step-by-step explanation:

23h - 13h + 11 = 8 ( subtract 11 from both sides )

10h = - 3 ( divide both sides by 10 )

h = - [tex]\frac{3}{10}[/tex]

Your answer(s) will be:

0.3 (Decimal Form)

              or

3/10 (Fraction Form)

Name the following triangle: 11in 77˚ 11in

Answers

Answer:

an acute triangle im guessing ik its not a right and the degrees and  the inches are small So it can't be absolute thats just what i was thinking but i might be wrong

Step-by-step explanation:

acute triangle because 77° is less than 90°, which would be a right triangle

201 ft
15 ft 6
200 ft
Find the perimeter of the triangle

Answers

Answer: 6416

Step-by-step explanation:

The perimeter of this triangle is 416 centimeters

[tex]\sf Solve\: this \: with\; steps:-[/tex]
[tex]\bf 4-7x=1-6x[/tex]

Answers

Answer:

x = 3

Explanation:

4 - 7(x) = 1 - 6(x)

-7(x) + 6(x) = 1 - 4

-(x) = -3

x = 3

Check:

4 -7(3) = 1-6(3)4 - 21 = 1 - 18-17 = -17

Hence, x = 3 confirmed as L.H.S = R.H.S

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \:4 - 7x = 1 - 6x[/tex]

[tex]\qquad \sf  \dashrightarrow \:4 - 1 = 7x- 6x[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 3[/tex]

so, we got the value of x as 3

Find the surface area

Answers

Answer: 343.5

Step-by-step explanation: multiply 15 * 17 and you get 255 then divide that by 2 and you get 127.5.

Next you multiply 8 by 27 (which is 216)

Now add 127.5 and 216 and you get 343.5

Consider the function. F(x, y) = 9x2y3 (a) find 3 f(x, y) dx

Answers

The integration of the function f(x, y) = 2x²y³ from 0 to 3 with respect to x is 27y³.

What is integration?

It is the reverse of differentiation.

The function f(x, y) is given below.

f(x, y) = 2x²y³

Then the integration of the function from 0 to 3 with respect to x.

[tex]\begin{aligned} \rm \int_{0}^{3}f(x, y)dx &= \rm \int_{0}^{3}9x^2y^3 dx \\\\&= \rm 9y^3 \ \int_{0}^{3} x^2 dx\\\\&= \rm 9y^3 (\dfrac{x^3}{3}) _{0}^{3}\\\\&= \rm3y^3 (3^3 - 0 ^3)\\\\&= \rm 3y^3 \times 9\\\\&= \rm 27y^3 \end{aligned}[/tex]

More about the integration link is given below.

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Evaluate:
(34x3)+7+ 24/6

Answers

Answer: 113 ( 34x3+11

Step-by-step explanation:

Step 1- Divide the numbers

34x 3 on top + 7 + 24/6

34 x 3 on top + 7 = 4

Step 2- Add the numbers

34 x 3 on top + 7 + 4

34 x 3 on top + 11

34 x 3 on top + 11

∠ AED is formed inside a circle by two intersecting chords. If minor arc BD = 70° and arc CA = 170° , what is the measure of ∠ AEC?

A)120
B)240
C)70
D)100

Answers

So

mCA=170°

And

mBD=70°

Now

180-170=10°

From mBD

70-10=60°

Now

m<AEC

70+50=120°

Option A

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