Question

each of the two congruent sides has length 13 cm. the third side has length blank cm. the perimeter of the triangle is 39 cm. (type integers or decimals.) (type an integer or a decimal.)

Explanation:

Step1: Recall perimeter formula

The perimeter $P$ of a triangle is $P=a + b + c$, where $a$, $b$, and $c$ are the side - lengths. In an isosceles triangle, two sides are congruent. Let the length of the congruent sides be $a=b = 13$ cm and the perimeter $P = 39$ cm.

Step2: Solve for the third side

We know that $P=a + b + c$. Substitute $a = 13$, $b = 13$, and $P = 39$ into the formula: $39=13 + 13 + c$.
First, simplify the right - hand side: $13+13 = 26$. So the equation becomes $39=26 + c$.
Then, solve for $c$ by subtracting 26 from both sides of the equation: $c=39 - 26$.
$c = 13$ cm.

Answer:

13