Question

Triangle A has sides of lengths `51`, `45`, and `33`. Triangle B is similar to triangle A and has a side of length `7`. What are the possible lengths of the other two sides of triangle B?

Answer 1

`color(brown)("Case - 1 : " 7, 9.55, 10.82`
`color(blue)("Case - 2 : " 7, 5.13, 7.93`
`color(crimson)("Case - 3 : " 7, 4.53, 6.18`

Explanation:

Since triangles A & B are similar, their sides will be in the same proportion.

`"Case - 1 : side 7 of " Delta " B corresponds to side 33 of " Delta " A`

`7 / 33 = b / 45 = c / 51, :. b = (45 * 7) / 33 = 9.55, c = (51 * 7) / 33 = 10.82`

`"Case - 2 : side 7 of " Delta " B corresponds to side 45 of " Delta " A`

`7 / 45 = b / 33 = c / 51, :. b = (7 * 33) / 45 = 5.13, c = (7 * 51) / 45 = 7.93`

`"Case - 3 : side 7 of " Delta " B corresponds to side 51 of " Delta " A`

`7 / 51 = b / 33 = c / 45, :. b = (7 * 33) / 51 = 4.53, c = (7 * 45) / 51 = 6.18`