Question

Triangle A has sides of lengths `1 ,4`, and `4`. Triangle B is similar to triangle A and has a side of length `3`. What are the possible lengths of the other two sides of triangle B?

Answer 1

The possible lengths of the DEF triangle are
`color(red)(3,12,12 )` & `color(blue)(3/4,3,3)`

Explanation:

Since the two triangles are similar, their corresponding sides are proportional.
Let the two triangles be ABC & DEF.

Then `a/d = b/e = c/f`
`a = 1, b = 4, c = 4`

If `d = 3`, then
`1/3 = 4/e = 4/f`
`:. e = 12, f = 12`

If `e = 3`, then
`4/3 = 1/d = 4/f`
`:. d = 3/4, f = 3`

The possible lengths of the DEF triangle are
`color(red)(3,12,12 )` & `color(blue)(3/4,3,3)`