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 other side?

Explanation:

Step1: Recall the perimeter formula

The perimeter \( P \) of a triangle is \( P=a + b + c \). For an isosceles triangle with two congruent sides \( a=b = 24 \) inches and perimeter \( P = 83 \) inches. Let the third - side be \( x \).

Step2: Substitute values into the formula

We have \( 83=24 + 24+x \).

Step3: Simplify the equation

First, calculate \( 24 + 24=48 \). So the equation becomes \( 83=48 + x \).

Step4: Solve for \( x \)

Subtract 48 from both sides: \( x=83 - 48 \).

Answer:

\( 35 \)