Question

if the sides of two similar triangles are in the ratio 12:13.find the ratio of their corresponding area

Answer 1

We know,
                The ratio of the area of two similar triangles is equal to the square of the ratio of their corresponding sides
 ∴ Ratio of the Area of the given similar triangles = 144 : 169  ( 12² : 13²)

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Answer 2

Let us assume the two Δ's be ΔABC and ΔDEF (refer added pic)

It is given that ΔABC similar to ΔDEF

We know that,

Ratio of Area of two similar Δ's is equal to the square of ratio of their

corresponding sides. (.i.e)

ar(ΔABC)/ar(ΔDEF) = (AB/DE)² = (AC/DF)² = (BC/EF)²

It is also give  given that ratio of corresponding sides is 12/13

Then,


ar(ΔABC)/ar(ΔDEF) = (12/13)²

                                 = 12² /13²
                                 
                                 = 144/169

Hence Ratio of Corresponding Area = 144:169

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