Question

A) For AQRS use the Triangle Proportionality Theorem to solve for x.

Answer 1

Answer:

a. x = 14

b. Perimeter = 77

Step-by-step explanation:

a. Based on the Triangle Proportionality Theorem:

$\frac{2x - 2}{13} = \frac{21 - 7}{7}$

$\frac{2x - 2}{13} = \frac{14}{7}$

$\frac{2x - 2}{13} = 2$

Cross multiply

$2x - 2 = 2(13)$

$2x - 2 = 26$

Add 2 to both sides

$2x = 26 + 2$

$2x = 28$

Divide both sides by 2

x = 14

b. Perimeter of ∆QRS = RQ + QS + RS = (2x - 2) + 13 + 17 + (21 - 7) + 7

Plug in the value of x

= (2(14) - 2) + 13 + 17 + 14 + 7

= 26 + 13 + 17 + 14 + 7

= 77