Question

The perimeters of two similar triangles are 25 cm and 15 cm respectively. If one side of first triangle is 9 cm, what is the corresponding side of the other triangle?

Answer 1

SOLUTION :

Given : Perimeter of two similar triangles are 25 cm, 15 cm and one of its side is 9 cm..

Let the two triangles be ABC & PQR.

Let one of its side is (AB) = 9 cm and the other side of other triangle be PQ.

Since the ratio of corresponding sides of similar triangles is same as the ratio of their perimeters.

∆ABC ∼ ∆PQR.

AB/PQ = BC/QR = AC/PR = 25/15

9/PQ = 25/15

25 PQ = 15 × 9

PQ = (15×9)/25

PQ =(3× 9 )/5

PQ = 27/5

PQ =  5.4 cm

Hence, the corresponding side of other ∆ is 5.4 cm.

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Answer 2

We know that once any two triangle are proved to be similar then we can say that the ratio of their perimeters is equal to the ratio of the corresponding sides.

Given,

Perimeter of bigger triangle, A = 25 cm
Perimeter of smaller triangle, B = 15 cm

Also,

One side of bigger triangle, C = 9 cm
Corresponding side of smaller triangle, D = ?

And,

A / B = C / D
25 / 15 = 9 / D

On cross - multiplying,

25D = 135
D = 135 / 25
D = 5.4 cm

Corresponding side of smaller triangle = 5.4 cm