(Q14) Explain why the triangles are similar and then find the value of x.

v)

PRQ515ABx4

Solution :

Given : In △PQR and △PMN

∠P = ∠P [∵ Common]

∠Q = ∠M [∵ Pair of corresponding angles for MN ∥ QR]

∠R = ∠N

△PQR ~ △PMN [∵ AAA similarity]

∴
PQ
PM
 =
QR
MN
 =
PR
PN
⇒
=
4 + x
 [From the figure, PR = 4 + x]

⇒ × = 4 + x

⇒ x = - =