Question

Three sides of a triangle measure 4,5 and 8. How do you find the length of the longest side of a similar triangle whose perimeter is 51?

Answer 1

The longest side is `24`.

Explanation:

The perimeter of the second triangle will be proportional to that of the first, so we'll work with that information.

Let the triangle with side lengths `4`, `5`, and `8` be called `Delta_A`, and the similar triangle with perimeter `51` be `Delta_B`. Let P be the perimeter.

`P_(Delta_A) = 4 + 5 + 8 = 17`

The expansion factor of the larger triangle relative to the smaller is given by `ƒ = (P_(Delta_B))/(P_(Delta_A))`, where `ƒ` is the expansion factor.

`ƒ= 51/17 = 3`

This result means that each of the sides of `Delta_B` measure `3` times the length of the sides of `Delta_A`.

Then the longest side in the similar triangle will be given by multiplying the largest side in the original triangle by the expansion factor, `3`.

Hence, the longest side in the similar triangle is `8 xx 3 = 24`.

Hopefully this helps!

Answer 2

24

Explanation:

The perimeter of the given triangle measures

`P=4+5+8=17`.

A similar triangle has proportional sides, so you can consider that the ratio of the perimeters is 51:17=3, and the same ratio is respect to the sides, so the lenght of the longest side of the similar triangle is 8 x 3 = 24