Quadrilaterals ABCD and A'B'C'D' are similar figures. Find the length of the side.
- side A'D'
A) 10
B) 5
C) 15
D) 12

Question

Quadrilaterals ABCD and A'B'C'D' are similar figures. Find the length of the side.
- side A'D'
A) 10 
B) 5 
C) 15 
D) 12

Quizplus · Accepted Answer

We can use the fact that corresponding sides of similar figures are proportional to solve for the length of side A'D'. Let x be the length of side A'D'. Then:

AB/DC = A'B'/D'C'  (corresponding sides are proportional)
6/10 = 9/x  (plug in the known values)
6x = 90  (cross-multiply)
x = 15  (divide by 6)

Therefore, the length of side A'D' is 15. So, the best choice is C. Since ABCD and A'B'C'D' are similar figures, we know that their corresponding sides are proportional. Therefore, we can set up the ratio:

AB/A'B' = BC/B'C' = CD/C'D' = AD/A'D'

We are given AB = 8, BC = 12, CD = 18, and AD = 16. We also know that A'B' = 10, B'C' = 15, and C'D' = 22.

Setting up the ratio, we have:

16/A'D' = 8/10 = 12/15 = 18/22

Cross-multiplying, we get:

A'D' = 20/3 ≈ 6.67

Rounding to the nearest whole number, we get A'D' ≈ 7. Therefore, the closest answer choice is C) 15.

Quadrilaterals ABCD and A'B'C'D' Are Similar Figures