Answer:
a. x = 14
b. Perimeter = 77
Step-by-step explanation:
a. Based on the Triangle Proportionality Theorem:
[tex] \frac{2x - 2}{13} = \frac{21 - 7}{7} [/tex]
[tex] \frac{2x - 2}{13} = \frac{14}{7} [/tex]
[tex] \frac{2x - 2}{13} = 2 [/tex]
Cross multiply
[tex] 2x - 2 = 2(13) [/tex]
[tex] 2x - 2 = 26 [/tex]
Add 2 to both sides
[tex] 2x = 26 + 2 [/tex]
[tex] 2x = 28 [/tex]
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
