# 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?

Aug 16, 2016

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 $8 \times 3 = 24$.

Hopefully this helps!

Aug 16, 2016

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