Question

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

b) After you have solved for x, what is the Perimeter of AQRS?

Answer 1

a. x = 14

b. Perimeter = 77

Explanation:

a. Based on the Triangle Proportionality Theorem:

`(2x - 2)/(13) = (21 - 7)/(7)`

`(2x - 2)/(13) = (14)/(7)`

`(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