Question

the length of two of the sides of the triangle. $p$ represents the total perimeter. find the measure of the third side.
$p=5x+2y$
the sides of the triangle are $x+2y$, $2x-3y$, and the third side is unknown.

Explanation:

Step1: Recall perimeter formula

Perimeter $P = \text{Sum of all sides}$
So, $\text{3rd side} = P - (\text{Side 1} + \text{Side 2})$

Step2: Substitute given expressions

$\text{3rd side} = (5x+2y) - [(x+2y)+(2x-3y)]$

Step3: Simplify inside parentheses

$(x+2y)+(2x-3y) = x+2x+2y-3y = 3x-y$

Step4: Subtract and simplify further

$\text{3rd side} = 5x+2y - (3x-y) = 5x+2y-3x+y = 2x+3y$

Answer:

$2x+3y$