The ratio of the measures of the sides of a triangle is 4:7:5. If the perimeter of the triangle is 128 yards, find the length of the longest side.

Hence, the length of the longest side is 56 yards.

Step-by-step explanation:

The ratio of the measures of the sides of a triangle is given as: 4:7:5.

Let 'x' denote a variable such that:

The length of first side of a triangle is 4x

the length of second side of a triangle is 7x

and the length of third side of a triangle is 5x.

also we are given that the perimeter of a triangle is 128 yards.

We know that the perimeter of a triangle is sum of lengths of all the sides of a triangle.

Hence, 4x+7x+5x=128 yards

⇒ 16x=128

on dividing both the sides by 16 we get

x=8.

Hence the length of first side of triangle is=4*8=32 yards

length of second side of triangle=7*8=56 yards

length of third side of a triangle=5*8=40 yards.

Hence, the length of the longest side is 56 yards.