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Question

Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

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Solution

Let ΔABC and ΔPQR be 2 similar triangles.

To prove : Ratio of areas of ΔABC and ΔPQR is equal to the square of the ratio of their corresponding sides.

Given : ΔABCΔPQR...(1)

ABPQ=BCQR=CARP...(2)

B=Q...(3)

In ΔABC and ΔPQS

B=Q [from (3)]

ADB=PSQ=90o

ΔABDΔPQS [ By AA similarity]

ABPQ=ADPS...(4)

AreaofΔABCAreaofΔPQR=12×BC×AD12×QR×PS

=BCQR×ADPS=ABPQ×ABPQ [From (2) & (4)]

=(ABPQ)2

1238483_1198134_ans_fcf16f99096549a3866096c4ce1b23ec.png

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