The areas of two similar triangles ABC and PQR are in the ratio 4 : 9. If the sum of the perimeters is 30 m, find the perimeter of each triangle.

Asked by Topperlearning User | 3rd Oct, 2017, 01:32: PM

Expert Answer:

Let x and y, s and t, u and v, be the corresponding sides of the triangles.

Then according to question,

begin mathsize 12px style 4 over 9 equals straight x squared over straight y squared equals straight s squared over straight t squared equals straight u squared over straight v squared
rightwards double arrow 2 over 3 equals straight x over straight y equals straight s over straight t equals straight u over straight v end style

So begin mathsize 12px style 2 over 3 end style= ratio of perimeters of triangles ABC and PQR

Let 2z and 3z be the respective perimeters.

So according to question 2z + 3z = 30

So z = 6

Hence the required perimeters are 12 cm and 18 cm.

Answered by  | 3rd Oct, 2017, 03:32: PM