Question

d) In the given figure, XY || PZ, then the measure of (q + r) is​

Answer 1

Answer:

Solution

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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]

PQ

PX

=

QR

XY

⇒

1+3

1

=

QR

XY

⇒

4

1

=

9

XY

⇒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)

=(

PQ

PX

)

2

⇒

ar(△PQR)

A

=

16

1

⇒ar(△PQR)=16A cm

2

Now, ar(trapeziumXYRQ)=(16A−A)cm

2

=15A cm

2

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Answer 2

Answer:

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