Question

the perimeter of a triangle is 80 centimeters. if two sides are equally long and the third side is 8 centimeters longer than the others, find the lengths of the three sides. the length of each of the two equally long sides is and the length of the longer side is

Explanation:

Step1: Let the length of each equal - side be $x$.

The length of the third side is $x + 8$.

Step2: Set up the perimeter equation.

The perimeter of a triangle is the sum of the lengths of its sides. So, $x+x+(x + 8)=80$.

Step3: Simplify the left - hand side of the equation.

Combining like terms, we get $3x+8 = 80$.

Step4: Isolate the variable term.

Subtract 8 from both sides: $3x=80 - 8=72$.

Step5: Solve for $x$.

Divide both sides by 3: $x=\frac{72}{3}=24$.

Step6: Find the length of the longer side.

The longer side is $x + 8=24 + 8=32$.

Answer:

The length of each of the two equally long sides is 24 centimeters and the length of the longer side is 32 centimeters.