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Question

"The ratio of areas of similar triangles is equal to the ratio of squares of corresponding side". Prove by using equilateral triangle scelane triangles.

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Solution

Ratio of area of similar is = ratio of square of corresponding sides
ABCsinPQR
ar(ABC)=12×B×H=12×BC×AK ----- (1)
ar(PQR)=12×B×H=12×QR×PL ----- (2)
Dividing (1) and (2)
ar(ABC)ar(PQR)=BC×AMQR×PN ------ (3)
In ABK and PQL
B=Q (angle of similar are equal )
M=N ( Both 90o)
ABKsinPQL ( By AA similarity )
ABPQ=AMPN {By CPCT } ------ (4)
ar(ABC)ar(PQR)=BCQR×ABPQ ------- (5) {from (3) and (4) }
arABCsinPQR
ABPQ=BCQR=ACPR
ar(ABC)ar(PQR)=AB×ABPQ×PQ=(ABPQ)2=(BCQR)2=(ACPR)2

1379335_1140975_ans_34c7541005fe48589aa476c14a693dd3.png

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