Question

What is the answer for number 8 and pls give step by step

Answer 1

Trapezoid 1 (left side):

Base 1 = 2

Base 2 = 5

Trapezoid 2 (right side):

Base 1 = 6

Base 2 = 8

Explanation:

1st trapezoid:

b_1 = x

b_2 = x + 3

h = 4

Hence, area (from formula) would be:

`A=(h)/(2)(b_1+b_2)\\A=(4)/(2)(x+x+3)\\A=2(2x+3)\\A=4x+6`

2nd trapezoid:

b_1 = 3x

b_2 = 4x

h = 2

Putting into formula, we get:

`A=(h)/(2)(b_1+b_2)\\A=(2)/(2)(3x+4x)\\A=1(7x)\\A=7x`

Let's equate both equations for area and find x first:

`4x+6=7x\\6=7x-4x\\6=3x\\x=(6)/(3)\\x=2`

We can plug in 2 into x and find length of each base of each trapezoid.

Trapezoid 1 (left side):

Base 1 = x = 2

Base 2 = x + 3 = 2 + 3 = 5

Trapezoid 2 (right side):

Base 1 = 3x = 3(2) = 6

Base 2 = 4x = 4(2) = 8