Question

What is the measure of the third side of a triangle if the Perimeter = 8x + 4y and two of the sides have measures of x + 2y and 3x + y?

Answer 1

Hello!

The answer is:

The third side measure is: 4x+y

Why?

We must remember that the perimeter of a triangle is equal to the sum of all of its three sides, so, using the given information, we have:

`Perimeter=a+b+c=8x+4y\\a=x+2y\\b=3x+y\\c=?`

So, we can calculate the measure of the third side using the following equation, and grouping the like terms, so:

`8x+4y=x+2y+3x+y+c\\c=8x+4y-x-2y-3x-y\\c=8x-x-3x+4y-2y-y\\c=8x-4x+4y-3y\\c=4x+y`

Have a nice day!