Question

both figures shown below are trapezoids. abcd ~ wxyz. what is the value of x? note: images are not to scale. trapezoid wxyz with sides: wz = 10 m, xy = 10 m, yz = 13 m, wx = x; trapezoid abcd with sides: da = 40 m, ab = 32 m, bc = 40 m, cd = 52 m

Explanation:

Step1: Find similarity ratio

$\text{Ratio} = \frac{WZ}{DA} = \frac{10}{40} = \frac{1}{4}$

Step2: Match corresponding sides

$\frac{x}{AB} = \frac{1}{4}$, substitute $AB=32$
$\frac{x}{32} = \frac{1}{4}$

Step3: Solve for x

$x = 32 \times \frac{1}{4}$

Answer:

8 m