Practice question — Given the trapezoid to the right find the length of legs in the following isosceles trapezoid
Answers
Given:
A figure of an isosceles trapezoid with bases 18 and 24, and the vertical height is 4.
To find:
The legs of the isosceles trapezoid.
Solution:
Draw another perpendicular and name the vertices as shown in the below figure.
From the figure it is clear that the AEFD is a rectangle. So,
[tex]EF=AD=18[/tex]
Since ABCD is an isosceles trapezoid, therefore in triangle ABE and DCF,
[tex]AB=DC[/tex] (Legs of isosceles trapezoid)
[tex]AE=DF[/tex] (Vertical height of isosceles trapezoid)
[tex]m\angle AEB=m\angle DFC[/tex] (Right angle)
[tex]\Delta ABE\cong \Delta DCF[/tex] (HL postulate)
[tex]BE=CF[/tex] (CPCTC)
Now,
[tex]BE+EF+FC=BC[/tex]
[tex]2BE+18=24[/tex]
[tex]2BE=24-18[/tex]
[tex]2BE=6[/tex]
[tex]BE=3[/tex]
Using Pythagoras theorem in triangle ABE, we get
[tex]Hypotenuse^2=Perpendicular^2+Base^2[/tex]
[tex](AB)^2=(AE)^2+(BE)^2[/tex]
[tex](AB)^2=(4)^2+(3)^2[/tex]
[tex](AB)^2=16+9[/tex]
[tex](AB)^2=25[/tex]
Taking square root on both sides, we get
[tex]AB=\pm \sqrt{25}[/tex]
[tex]AB=\pm 5[/tex]
Side length cannot be negative. So, [tex]AB=5[/tex].
Therefore, the length of legs in the given isosceles trapezoid is 5 units.
Related Questions
a loan of $10,000 was granted for 9 year at 8 percent simple interest .what is the amount of simple interest owed
Answers
Answer:
7200
Step-by-step explanation:
principle=10000
time=9
rate=8%
now
simple interesr=p*t*r/100
= 10000*9*8/100
=7200
I NEED HELP WITH THIS MATH PROBLEM
Answers
Answer:
Step-by-step explanation:
9.8 divided by 100
Answer 0.098 km/liter
Given the isosceles trapezoid EFGH and side length JL = 93 units. If the length of KN = (3x + 1) and MN = (5x - 4), what is the length of KM?
Answers
Answer:
KM=JL=93 units
or KM=KN + MN= 8x-3
Step-by-step explanation:
The value of length of KM can be equal to either JL or obtained by adding KN = (3x + 1) and MN = (5x - 4) depending on the diagram.
An isosceles trapezoid has non parallel sides congruent.
In the isosceles trapezoid the diagonals are also equal.
There is a pair of parallel lines in an isosceles trapezoid.
In the 1st figure trapezoid JL and KM are diagonals.
If we take the JM and KL to be the parallel lines then the opposite sides can be JK and LM
And N is the middle line or the mid segment.
In the figure 2
The value of length of KM is obtained by adding KN = (3x + 1) and MN = (5x - 4)
KM=KN + MN = (5x - 4) +(3x + 1)
KM=8x- 3
If x = 2, y = 3 and z = 4, calculate the value of each of the following algebraic expression: 3x + 3y =
Answers
3(2) + 3(3)
6 + 9
15
Ashley needs to drive 17 miles to work. So far, she has driven 7.2 miles. How many more miles must she drive?
Answers
9514 1404 393
Answer:
9.8 miles
Step-by-step explanation:
The number of miles to go is the difference between the miles to work and the miles traveled so far:
17 -7.2 = 9.8 . . . miles to go
?????????????????????????????????????????????????????????????????????????????
Answers
Answer:
A≈259.37.....Tell me its it wrog
Step-by-step explanation:
Use the distributive property to simplify each expression.
(-5d + 1) (-2)
Answers
Answer: 10d-2
Step-by-step explanation:
Answer:
10d - 2
Step-by-step explanation:
Multiply each term inside parentheses by -2, separately:
10d - 2 (answer)
Sammie cuts a piece of ribbon that is 2 feet long.
She needs only 18 inches of ribbon.
How much extra ribbon did she cut?
Answers
Answer:
the answer is 6 extra inches
Step-by-step explanation:
im assuming she cut off 2 feet of ribbon which is also known as 24 inches so the you just do 24 - 18 = 6
PLSSSSS HELP!!!!!!!!!
Answers
Answer:
x=30º
∠CAB=60°
∠ACB=80°
Step-by-step explanation:
Because the angles of every triangle add up to 180º, we know that:
[tex]2x+20+2x=180-40\\ 4x=180-40-20\\ 4x=180-60\\ 4x=120\\ x=\frac{120}{4}[/tex]
x=30º
Plug that in for x on both angles, and you will get
∠CAB=60°
∠ACB=80°
what expression is the sane as 1/2 x 5
Answers
Answer:
5 divided by 2
Step-by-step explanation:
1/2 * 5 = 5/2
5/2 = 5 divided by 2
Multiply the two binomials.
(3x + 5)(4x - 1)
HELP PLS
Answers
Answer:
12x² + 17x - 5
Step-by-step explanation:
Given
(3x + 5)(4x - 1)
Each term in the second factor is multiplied by each term in the first factor, that is
3x(4x - 1) + 5(4x - 1) ← distribute parenthesis
= 12x² - 3x + 20x - 5 ← collect like terms
= 12x² + 17x - 5
Which of these might describe expenses for a student? Select all that apply.
donations
food
shoes
allowance
savings
gift received
Answers
Answer:
Foods and shoes thats it
Step-by-step explanation:
Santiago gave out a survey to some students in his school about their favorite color. 429 of those surveyed said their favorite color was blue. If 55% of the students surveyed said their favorite color was blue, how many students were surveyed in total?
Answers
Answer:
780
Step-by-step explanation:
1/8 quarters is how many gallons
Answers
Answer:
4 quarters in a gallon
Step-by-step explanation:
What is the common ratio of the sequence?
-2, 6, -18, 54
Answers
Answer:
The common ratio of the sequence is -3
Step-by-step explanation:
The reason why the answer is -3 because every single number is multiplied by -3. If you need an explanation on how I found it, here it is:
To determine the common ratio by dividing each number in the sequence from the number preceding it. If the same number is not multiplied to each number in the series, then there is no common ratio.
What is the value of x in the equation One-third x minus two-thirds = negative 18?
–56
–52
52
56
Answers
Answer:
-52, I think
Step-by-step explanation:
The diameter of a circle is 6 cm. About how long is the circumference of the circle?
A
9 cm
(B
12 cm
©
(U
19 cm
D
28 cm
Answers
Answer:
The circumference is about 19 centimeters.
Step-by-step explanation:
The formula for finding the circumference of a circle is [tex]2\pi r[/tex] or simply [tex]\pi d[/tex].
Now input the values into the formula, keeping in mind that pi is almost 3.14.
[tex]\pi *6=18.84[/tex]
Answer ≈ 19 cm
Hope this helps; have a great day!
draw the grid of 3y- 4x=12
Answers
A photo of an ant in a science book is increased to 655% as large as the actual size. If the ant is 14 millimeters, what is the size of the ant in the photo?
Answers
Answer: [tex]91.7\ mm[/tex]
Step-by-step explanation:
Given
The size of the ant is enlarged by [tex]655\%[/tex]
The actual size of the ant is [tex]14\ mm[/tex]
Enlarged size is
[tex]\Rightarrow 14\times \dfrac{655}{100}\\\\\Rightarrow 91.7\ mm[/tex]
Each big square below represents one whole.
What percent is represented by the shaded area?
Answers
Answer:
173%
Step-by-step explanation:
I think?
1. x2 + 9x + 20
2. x2 + 7x + 12
3. x2 + 8x + 15
4. x2 + 7x + 12
5. x2 + 11x + 10
6. x2 + 7x + 6
7. x2 + 5x + 4
8. x2 + 10x + 21
9. x2 + 10x + 16
10. x2 + 10x + 9
11. x2 + 12x + 20
12. x2 + 15x + 14
13. x2 + 13x + 42
14. x2 + 9x + 18
15. x2 + 16x + 60
Answers
Answer:
1) (x+5)(x+4)
Step-by-step explanation:
Which rectangular prism has a surface area of 62 square units? [Note: Art is not drawn to scale.]
Answers
Answer:
the Answer is C
Step-by-step explanation
just took the test
Answer:
C
Step-by-step explanation:
I got it right
The amount of medication in a patient's bloodstream decreases exponentially from the time the medication is administered. A patient is administered a 300 mg dose of medication that decreases by 25% in the bloodstream each hour. Which function models this situation?
Answers
A deli is offering two specials. The roast beef special gives a profit of $2.30 per sandwich, and the turkey special gives a profit of $3.10 per sandwich. The roast beef special uses two slices of bread and three slices of cheese. The turkey special uses two slices of bread and four slices of cheese. The deli has 120 slices of bread and 160 slices of cheese available for the specials. The deli wants to maximize its profit selling specials. Let x represent the number of roast beef specials and y represent the number of turkey specials. What are the constraints for the problem?
Answers
Answer:
The constraints are as follows;
1) 2·x + 2·y ≤ 120
2) 3·x + 4·y ≤ 160
3) x = 2.30
4) y = 3.10
5) P = 2.3·x + 3.10
Step-by-step explanation:
The question is a word problem, with the analysis as follows;
The profit from the roast beef special per sandwich = $2.30
The profit from the turkey special per sandwich = $3.10
The number of slices of bread in the roast beef special = Two slices
The number of slices of cheese in the roast beef special = Three slices
The number of slices of bread in the turkey special = Two slices
The number of slices of cheese in the turkey special = Four slices
The number of slices of bread the deli has = 120 slices
The number of slices of cheese the deli has = 160 slices
Let 'x' and represent the number of roast beef special and 'y' represent the number of turkey special the deli makes, then we have the constraints as follows;
For the number of slices of bread used;
2·x + 2·y ≤ 120...(1)
For the number of slices of cheese used;
3·x + 4·y ≤ 160...(2)
x = 2.30
y = 3.10
The profit 'P' is given by the following equation
P = 2.3·x + 3.10.
Answer:
its a
Step-by-step explanation:
trust
The table shows the relationship y = kx.
what is the constant of proportionality, k?
A. 1/5
B. 3/5
C. 5/3
D. 1/3
Answers
Television sizes are described by the length of their diagonal measure. What would be the listed size of the TV shown? (To the nearest whole inch)
Answers
Answer:
The listed size is 32 inches
Step-by-step explanation:
Given
See attachment for television
Required
The listed size
The listed size is calculated by the diagonal of the television.
This is calculated as using Pythagoras theorem as follows:
[tex]Diagonal^2 = Length1^2 + Length2^2[/tex]
Where:
[tex]Length1 =28in[/tex]
[tex]Length2 =15.7in[/tex]
So, we have:
[tex]Diagonal^2 = 28^2 + 15.7^2[/tex]
[tex]Diagonal^2 = 784 + 246.49[/tex]
[tex]Diagonal^2 = 1030.49[/tex]
Take positive square roots of both sides
[tex]Diagonal = \sqrt{1030.49[/tex]
[tex]Diagonal = 32[/tex] --- approximated
Hence, the listed size is 32 inches
In the library where you work, it usually takes you 2 hours to shelve 5 carts of books. At this rate, about how many minutes should it take you to shelve 1 cart of
books?
Answers
Answer: 24 min
Step-by-step explanation:
2 hrs / 5 carts = 120 min / 5 carts
120 / 5 = 24 min / 1 cart
Look at the equation below.
77 +9y = 4
What is the value of y?
4 -9
B -8.1
с 9
D 21.5
Answers
A person is designing a new rectangular garden. Its area must be 344 square feet. List the length and width, in feet, of all the possible gardens with this area. Use whole-number dimensions. Which garden has the least perimeter?
Answers
Answer:
(1 x 344) ft
(344 x 1) ft
(2 x 172) ft
(172 x 1) ft
(4 x 86) ft
(86 x 4) ft
(8 x 43) ft
(43 x 8) ft
the garden with the least perimeter is the garden with dimensions 8 x 43
Step-by-step explanation:
area of a rectangle = length x width
given the area, we can determine the dimensions of the rectangle by calculating the factors of 344. the factors are then multiplied to determine the area
factors of a number are numbers that divide the original number evenly. they are numbers that when used to divide another number, we derive only only numbers
Factors of 344 = 1, 2,2,2,43 and 344
Possible dimensions and their areas
1 x 344 = =344 ft²
2 x 172 = 344 ft²
4 x 86 = 344 ft²
8 x 43 = 344 ft²
Perimeter of a rectangle = 2 x (length + width)
i would use the dimensions i calculated to determine all the possible perimeters
2 x ( 1 + 344) = 690 ft
2 x (2 + 172) = 348 ft
2 x (4 + 86) = 180 ft
2 x (8 + 43) = 102 ft
the garden with the least perimeter is the garden with dimensions 8 x 43
IDENTIFICA EL VOLUMEN DE CADA UNA DE LAS SIGUIENTES FIGURAS
Answers
Answer:
Não falo espanhoooooooooooooooool
