Answer:
x = 15
Step-by-step explanation:
Given that ∆PQR ~ ∆SQT, therefore their side lengths are proportional to each other.
Thus:
[tex] \frac{PQ}{SQ} = \frac{PR}{ST} [/tex]
PQ = (x + 5) + 8 = x + 13
SQ = 8
PR = 21
ST = x - 9
Plug in the values
[tex] \frac{x + 13}{8} = \frac{21}{x - 9} [/tex]
Cross multiply
[tex] (x + 13)(x - 9) = 8*21 [/tex]
[tex] x(x - 9) +13(x - 9) = 168 [/tex]
[tex] x^2 - 9x + 13x - 117 = 168 [/tex]
[tex] x^2 + 4x - 117 = 168 [/tex]
Subtract 168 from both sides
[tex] x^2 + 4x - 117 - 168 = 0 [/tex]
[tex] x^2 + 4x - 285 = 0 [/tex]
Factorize
[tex] x^2 + 19x - 15x - 285 = 0 [/tex]
[tex] x(x + 19) - 15(x + 19) = 0 [/tex]
(x + 19)(x - 15) = 0
x = -19 or x = 15
