If the perimeter of a triangle is 10x + 5y and two of the sides are 3x + 4y and 5x − y, which is the third side? a. 2x + 2y b. 2x + y c. −2x + 2y d. x + 2y

The measures of two sides of a triangle are 3x + 4y and 5x - y. If the perimeter is 10x + 5y, find the measure of the third side. 

Let measure of the 3rd side be 'b'. 

Substitute the values of length of the two sides and perimeter in equation and solve for b. 

So, 10x + 5y = 3x + 4y + 5x - y + b[Substitute the values] 
10x + 5y = 8x + 3y + b 
(10x + 5y) - (8x + 3y) = b 
10x + 5y - 8x - 3y = b 
10x - 8x + 5y - 3y = b 
2x + 2y = b 

So, the measure of the third side is 2x + 2y. 

The answer is option c.