Question

two sides of a triangle have the same length. the third side measures 3 m less than twice the common length. the perimeter of the triangle is 21 m. what are the lengths of the three sides? what is the length of the two sides that have the same length?

Explanation:

Step1: Let the common length be $x$.

Let the length of the two equal - sided be $x$ meters each. The third side is $(2x - 3)$ meters.

Step2: Set up the perimeter equation.

The perimeter of a triangle is the sum of the lengths of its sides. So, $x + x+(2x - 3)=21$.

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

Combining like terms, we get $4x-3 = 21$.

Step4: Add 3 to both sides of the equation.

$4x-3 + 3=21 + 3$, which simplifies to $4x=24$.

Step5: Solve for $x$.

Dividing both sides by 4, we have $x = 6$.

Answer:

6