Question

Triangle A has sides of lengths `32`, `36`, and `16`. Triangle B is similar to triangle A and has a side of length `8`. What are the possible lengths of the other two sides of triangle B?

Answer 1

Case 1 : `Delta B = color(green)(8, 18, 16`

case 2 : `Delta B = color(brown)(8, 9, 4`

Case 3 : `Delta B = color(blue)(8, 32/9. 64/9`

Explanation:

Case 1 : side 8 of triangle B corresponding to side 16 in triangle A

`8 / 16 = b / 36 = c / 32`

`b = (cancel(36)^color(green)18 * cancel8) / cancel16^color(red)cancel2`

#b = 18,

`c = (cancel(32)^color(green)16 * cancel8) / cancel16^color(red)cancel2`

`c = 16`

Similarly,Case 2 : side 8 of triangle B corresponding to side 32 in triangle A

`8 / 32 = b / 36 = c / 16`

`b = 9, c = 4`

Case 3 : side 8 of triangle B corresponding to side 36 in triangle A

`8 / 36 = b / 16 = c / 32`

`b = 32/9, c = 64/9`