Question

prove that ratio of areas of two similar triangles is equal to square the ratio of their perimeters

Answer 1

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Answer 2

Answer:

(Perimeter of triangle (ABC/ PQR) )² =  Area ( ABC / P QR )

Step-by-step explanation:

The ratio of areas of two similar triangles is equal to square the ratio of their perimeters.

Draw two triangle likewise, ABC and P QR such that they are similar with each other.

As we know that the ratio of area of similar triangle is equal to the square of the ratio of their corresponding sides.

( Area ( ABC / P QR ) = ( AB/PQ)² = (BC/ QR)² = ( AC/PR)²......................i

Perimeter of triangle (ABC/ PQR) = (AB + BC + CA / PQ + QR + RP)

(Perimeter of triangle (ABC/ PQR) )² =  Area ( ABC / P QR )

Hence Proved