Question

Triangle A has sides of lengths `24`, `15`, and `21`. Triangle B is similar to triangle A and has a side of length `24`. What are the possible lengths of the other two sides of triangle B?

Answer 1

Case 1 : `color(green)(24, 15,21` Both are identical triangles

Case 2 : `color(blue)(24, 38.4, 33.6`

Case 3 : `color(red)(24, 27.4286, 17.1429`

Explanation:

Given :Triangle A (`DeltaPQR`) similar to Triangle B `(DeltaXYZ)`

`PQ = r = 24, QR = p = 15, RP = q = 21`

Case 1 : `XY = z = 24`

Then using similar triangles property,

`r / z = p / x = q / y`

`24 / 24 = 15 / x = 21 / y`

`:. x = 15, y = 21`

Case 2 : `YZ = x = 24`

`24 / z = 15 / 24 = 21 / y`

`z = (24 * 24) / 15 = 38.4`

`y = (21 * 24) / 15 = 33.6`

Case 2 : `ZX = y = 24`

`24 / z = 15 / x = 21 / 24`

`z = (24 * 24) / 21 = 27.4286`

`y = (15 * 24) / 21 = 17.1429`