Question

the perimeter of an isosceles triangle is 83 inches. each of the two congruent sides of the triangle has a length of 24 inches. what is the length, in inches, of the third side?

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 with two congruent sides of length $a=b = 24$ inches and perimeter $P = 83$ inches, we substitute into the formula.
$P=a + b + c$ becomes $83=24 + 24 + c$.

Step2: Simplify the right - hand side

First, add the two known side - lengths: $24+24 = 48$. So the equation is $83=48 + c$.

Step3: Solve for $c$

Subtract 48 from both sides of the equation: $c=83 - 48$.
$c = 35$.

Answer:

35