Question

Unit 6 homework 2 need help

Answer 1

∆PQR and ∆SQT are similar, so corresponding sides occur in fixed ratios with one another. This means

SQ / PQ = ST / PR

Solve for x :

8 / ((x + 5) + 8) = (x - 9) / 21

8 / (x + 13) = (x - 9) / 21

168 = (x - 9) (x + 13)

168 = x² + 4x - 117

x² + 4x - 285 = 0

(x + 19) (x - 15) = 0

⇒   x = -19   or   x = 15

But x can't be smaller than 9, otherwise ST = x - 9 would be a negative length. So x = 15.