Question

in triangle pqr py =10, pq=50 , PR=20 YQ= 30 WHERE line xy parallel side be?

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Answer 1

Answer:

In △PXY and △PQR,XY is parallel to QR, so corresponding angles are equal.

∠PXY=∠PQR

∠PYX=∠PRQ

Hence, △PXY∼△PQR     [By AA similarity criterion]

PQPX=QRXY

⇒1+31=QRXY

⇒41=9XY

⇒XY=2.25 cm

We know that the ratio of areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.

ar(△PQR)ar(△PXY)=(PQPX)2

⇒ar(△PQR)A=161

⇒ar(△PQR)=16A cm2

Now, ar(trapeziumXYRQ)=(16A−A)cm2=15A cm2