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faust18 [17]
2 years ago
9

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

Mathematics
1 answer:
xenn [34]2 years ago
8 0

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

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