Question

the triangle shown is isosceles. find the length of each side and the perimeter. each of the two congruent sides has length (type integers or decimals.) the third side has length (type an integer or a decimal.) the perimeter of the triangle is 39 cm.

Explanation:

Step1: Recall perimeter formula

The perimeter $P$ of a triangle is $P=a + b + c$, where $a$, $b$, $c$ are the side - lengths. In an isosceles triangle, two sides are congruent. Let the congruent sides have length $x$ and the third side have length $y$. So $P = 2x + y$.

Step2: Substitute known values

We know that $P = 39$ cm and $x = 13$ cm. Substitute into the perimeter formula: $39=2\times13 + y$.

Step3: Solve for the third - side length

First, calculate $2\times13 = 26$. Then the equation becomes $39=26 + y$. Subtract 26 from both sides: $y=39 - 26$. So $y = 13$ cm.

Answer:

13