A triangle has a perimeter of 126 centimeters. The 2 longer sides are 3 times as long as the shortest side. Find the length of each side.

The shorter side of the triangle is 18 cm and each of the longer sides are 54 cm

Solution:

Given that triangle has perimeter of 126 cm

Let the length of the shorter side of the triangle be "a"

The 2 longer sides are 3 times as long as the shortest side

So length of 2 longer sides = 3 (length of the shorter side)

length of 2 longer sides = 3a

The perimeter of triangle is given as:

perimeter of triangle = length of the shorter side + length of 2 longer sides

perimeter of triangle = a + 3a + 3a

126 = a + 3a + 3a

7a = 126

a = 18

So length of shorter side = 18 cm

length of 2 longer sides are each = 3a = 3 (18) = 54 cm

Thus, the shorter side of the triangle is 18 cm and each of the longer sides is 54 cm