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
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 xx 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