Question

Triangle A has sides of lengths `24`, `24`, and `20`. Triangle B is similar to triangle A and has a side with a length of `16`. What are the possible lengths of the other two sides of triangle B?

Answer 1

Lengths of other two sides of triangle B are `16` & `13(1/3)`

Explanation:

Triangle A & B are similar. Hence corresponding angles are equal and ratio of the corresponding sides are equal.
Let the vertices of Triangle A & B be PQR & XYZ respectively.

Given `PQ=24, QR=24` & `RP=20`
Also `(PQ)/(XY)=(QR)/(YZ)=(RP)/(ZX)`

If `XY=16` then
`24/16=24/(YZ)=20/ZX`
`:.YZ=(24*16)/24=16`
Similarly `ZX=(20*16)/24=40/3`