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If two triangles are similar, then the ratio of their areas will equal to ratio of the corresponding sides.(a) True(b) FalseI had been asked this question in an online interview.This interesting question is from Area of Similar Triangle in section Triangles of Mathematics – Class 10

Answer»

Right choice is (B) False

Easiest explanation: RATIO of similar triangles is equal to the square of their sides.

Since, ∆ABC ∼ ∆PQR, so they are equiangular and their sides are proportional.

∴ \(\frac {AB}{PQ}=\frac {AC}{PR}=\frac {BC}{QR}\), ∠A = ∠P, ∠B = ∠Q, ∠C = ∠R

\( \frac {area \, of \, triange \, ABC}{area \, of \, triange \, PQR}=\frac {\frac {1}{2} \times BC \times AD}{\frac {1}{2} \times QR \times PS}=\frac {BC \times AD}{QR \times PS}\)

Now, ∆ADB and ∆PS,

∠ABD = ∠PQS

∠B = ∠Q

Hence, ∆ABC ∼ ∆PQS

So, \( \frac {AD}{PS}=\frac {AB}{PQ}\)

But, \( \frac {AB}{PQ}=\frac {BC}{QR}\)

∴ \( \frac {AD}{PS}=\frac {BC}{QR}\)

\( \frac {area \, of \, triange \, ABC}{area \, of \, triange \, PQR}=\frac {\frac {1}{2} \times BC \times AD}{\frac {1}{2} \times QR \times PS}=\frac {BC^2}{QR^2}\)


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