Question

Triangle A has sides of lengths `36`, `32`, and `24`. 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

The other two possible sides are `color(red)(3.bar 5` and `color(blue)(2.bar 6`

Explanation:

We know the sides of triangle A,But we know only one side of triangle B

Consider,

We can solve for the other two sides using the ratio of the corresponding sides

Solve,

`color(red)(x`

`rarr36/4=32/x`

`rarr9=32/x`

`color(green)(rArrx=32/9=3.bar 5`

`color(blue)(y`

`rarr36/4=24/y`

`rarr9=24/y`

`color(green)(rArry=24/9=2.bar 6`