Question

1. the perimeter of an isosceles triangle is 19x + 9 inches. the side that is not congruent to the other two sides has a length of 9x - 4 inches. what if the length of the two congruent sides?

Explanation:

Step1: Define congruent side length

Let $s$ = length of one congruent side.

Step2: Set up perimeter equation

Perimeter = sum of all sides:
$$19x + 9 = 2s + (9x - 4)$$

Step3: Isolate the term with $s$

Subtract $9x - 4$ from both sides:
$$19x + 9 - (9x - 4) = 2s$$
$$19x + 9 - 9x + 4 = 2s$$
$$10x + 13 = 2s$$

Step4: Solve for $s$

Divide both sides by 2:
$$s = \frac{10x + 13}{2} = 5x + \frac{13}{2}$$

Answer:

The length of each congruent side is $\boldsymbol{5x + \frac{13}{2}}$ inches (or $\boldsymbol{\frac{10x + 13}{2}}$ inches).