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D) In the given figure, XY || PZ, then the measure of (q + r) is |
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Answer» SolutionverifiedVerified by TopprIn △PXY and △PQR,XY is parallel to QR, so corresponding angles are equal.∠PXY=∠PQR∠PYX=∠PRQHence, △PXY∼△PQR [By AA similarity CRITERION]PQPX = QRXY ⇒ 1+31 = QRXY ⇒ 41 = 9XY ⇒XY=2.25 cmWe 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 cm 2 Now, ar(trapeziumXYRQ)=(16A−A)cm 2 =15A cm 2 Was this ANSWER helpful? |
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