(Q10) Explain why the triangles are similar and then find the value of x.

i)

PS5QRLT34.5x

Solution :

Given : In △PQR and △LTS

∠Q = ∠T; ∠R = ∠S = 90°

∴ ∠P = ∠T

(by angle sum property of triangles)

Hence, △PQR ~ △LTS [∵ AAA]

Then
PQ
LT
 =
QR
TS
 =
PR
LS
∴
=
x
⇒ x =
×
3
 = × =