Question

Given: a trapezoid with b1 and b2 as the length of the bases, h as the length of the altitude, and A as the area. Click on the graphic next to the "h" to choose the correct value based on the given values of b1, b2, and A.

b1 =5 sqrt 2
b2 = 3 sqrt 2
A = 4 sqrt 6
h =

Answer 1

5 sqrt 7.5 is to the h

Answer 2

√3

Explanation:

The formula for the area of a trapezoid is

`A=(1)/(2)(b_1+b_2)h`

Plugging in our information, we have

`4√(6)=(1)/(2)(5√(2)+3√(2))h`

Combining like terms in parentheses, we have

`4√(6)=(1)/(2)(8√(2))h`

To cancel the 1/2, we will multiply both sides by 2:

`4√(6)* 2=(1)/(2)(8√(2))h* 2\\\\8√(6)=8√(2)(h)`

Divide both sides by 8:

`(8√(6))/(8)=(8√(2)(h))/(8)\\\\√(6)=√(2)(h)`

Divide both sides by √2:

`(√(6))/(√(2))=(√(2)(h))/(√(2))\\\\(√(6)√(2))/(√(2)√(2))\\\\=(√(12))/(2)\\\\=(√(4*3))/(2)\\\\=(2√(3))/(2)\\\\=√(3)`