Question

Triangle A has sides of lengths `28`, `32`, and `24`. Triangle B is similar to triangle A and has a side of length `4`. What are the possible lengths of the other two sides of triangle B?

Answer 1

Case 1 : sides of Triangle B `4, 4.57, 3.43`

Case 2 : sides of Triangle B `3.5, 4, 3`

Case 3 : sides of Triangle B `4.67, 5.33, 4`

Explanation:

Triangle A with sides `p = 28, q = 32, r = 24`

Triangle B with sides `x, y, z`

Given both the sides are similar.

Case 1. Side x = 4 of triangle B proportional to p of triangle A.

`4 / 28 = y / 32 = z / 24`

`y = (4 * 32) / 28 = 4.57`

`z = (4 * 24) / 28 = 3.43`

Case 2 : Side y = 4 of triangle B proportional to q of triangle A.

`x / 28 = 4 / 32 = z / 24`

`x = (4 * 28) / 32 = 3.5`

`z = (4 * 24) / 32 = 3`

Case 3 : Side z = 4 of triangle B proportional to r of triangle A.

`x / 28 = y / 32 = 4 / 24`

`x = (4 * 28) / 24 = 4.67`

`y = (4 * 32) / 24 = 5.33`