Question

Prove that the ratio of the perimeters of two similar triangles is the
same as the ratio of their corresponding sides.
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Answer 1

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Let the 2 similar△les be△ABC&△PQR.

When △les are similar,

1.The corresponding angles are equal.

2.Their corresponding sides are proportional.

hence in △ABC&△PQR

AB/PQ=BC/QR=AC/PR

The perimeter of △ABC,

=AB+BC+AC−(i)

The perimeter of △PQR,

=PQ+QR+PR−(ii)

∴AB/PQ=BC/QR=AC/PR=AB+BC+AC/PQ+QR+PR

= Perimeter of △ABC/Perimeter of △PQR