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The perimeters of two similar triangles ...

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?

A

`15/7`

B

`17/7`

C

`27/5`

D

`17/5`

Text Solution

Verified by Experts

The correct Answer is:
C
Let AB= 9 cm
since `triangleABC~ trianglePQR` (given)
`(AB)/(PQ)=(BC)/(QR)=(AC)/(PR) = k` (say) ….(1)
corresponding sides of similar triangles are proportional)
AB=k. PQ, BC=k.QR,AC=k.PR
`("perimeter of"triangleABC)/("perimeter of"trianglePQR)=(AB+BC+CA)/(PQ+QR+RP)=(k.PQ+.k.QR+k.PR)/(PQ+QR+RP)`
`(k(PQ+QR+RP))/((PQ+QR+RP))`
= k
from (1) and (2) , we get
`(AB)/(PQ)=(BC)/(QR)=(AC)/(PR)= ("perimeter" (triangleABC))/("perimeter"(trianglePQR))`
`9/(PQ)= 25/15 Rightarrow PQ = (9xx15)/25= 5.4`
Hence, the corresponding side of the second triangle is 5.4cm.
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