# 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?

##### 2 Answers

The longest side is

#### 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

The expansion factor of the larger triangle relative to the smaller is given by

This result means that each of the sides of

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

Hence, the longest side in the similar triangle is

Hopefully this helps!

24

#### Explanation:

The perimeter of the given triangle measures

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