Question

Triangle A has sides of lengths `36`, `44`, and `32`. 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

Possible lengths of other two sides of triangle B are

Case 1 : `4.8889, 3.5556`

Case 2 : `3.2727, 2.9091`

Case 3 : `4.5, 5.5`

Explanation:

Let the sides be a1, a2, a3 of `Delta`A and b1, b2, b3 of `Delta` B.

We know,

`(a1) / (b1) = (a2) / (b2) = (a3) / (b3)`

Given `a1 = 36, a2 = 44, a3 = 32`

Case 1 :
`b1 = 4`

Then `b2 = ((a2) * (b1)) / (a1) = (44*4)/36 = 4.8889`

`b3 = ((a3) * (b1)) / (a1) = (32 * 4) / 36 = 3.5556`

Case 2 :
`b2 = 4`

`b1 = ((a1)*(b2)) / (a2) = (36*4)/44 = 3.2727`

`b3 = (32 * 4) / 44 = 2.9091`

Case 3 :

`b3 = 4`

`b1 = (36 * 4) / 32 = 4.5`

`b2 = (44 * 4) / 32 = 5.5`