QuestionThe perimeter of a triangle is $10 x+3 y$. The length of two sides of the triangle are $3 x-y$ and $5 x+2 y$. Find the measure of the third side of the triangle.

Studdy Solution
To find the third side, we need to isolate it in the equation. First, simplify the equation by combining like terms:
$$10x + 3y = 3x - y + 5x + 2y + (\text{third side})$$ $$10x + 3y = (3x + 5x) + (-y + 2y) + (\text{third side})$$ $$10x + 3y = 8x + y + (\text{third side})$$
Now, solve for the third side by subtracting $8x + y$ from both sides:
$$\text{third side} = 10x + 3y - 8x - y$$
Simplify the expression:
$$\text{third side} = (10x - 8x) + (3y - y)$$ $$\text{third side} = 2x + 2y$$
The measure of the third side of the triangle is:
$$\boxed{2x + 2y}$$