a triangle has a perimeter of 126 centimeters, each of the 2 longer sides of the triangle is three times as long as the shortest side. Find the length of each side of the triangle.

shortest side --- x

each of the other sides --- 3x

x + 3x + 3x = 126
7x = 126

carry on ....

To find the length of each side of the triangle, let's assign variables to the lengths of the sides.

Let's call the shortest side "x".

According to the given information, the two longer sides of the triangle are three times as long as the shortest side. So, their lengths can be denoted as "3x" and "3x".

The perimeter of a triangle is the sum of the lengths of its sides. Therefore, we can write an equation:

x + 3x + 3x = 126

Simplifying the equation:

x + 9x = 126

Combining like terms:

10x = 126

To solve for "x", divide both sides of the equation by 10:

x = 126 / 10

x = 12.6

Now, we can find the lengths of the other two sides by substituting the value of "x" back into "3x":

Length of the longer sides = 3 * 12.6 = 37.8

Therefore, the lengths of the sides of the triangle are:
Shortest side = 12.6 cm
Longer sides (2 sides) = 37.8 cm each