Finding the missing side of a triangle.

Question

If one side of a triangle is 3x+4y, another side is 5×-y and the perimeter is 10x+5y. What is the measurement of the missing side?

Answer 1

If one side of a triangle is 3x+4y, another side is 5x-y and the perimeter is 10x+5y. What is the measurement of the missing side?

Since the perimeter of any figure is the sum of all its sides, we can set up an equation representing the perimeter of our triangle:

P = side a + side b + side c or simply P = a+ b + c

The perimeter of 10x + 5y is given, substitute in for P, while replacing two of the sides, a and b, with 3x+4y and 5x-y

So, 10x + 5y = 3x + 4y + 5x - y + c Where c = 3rd side

Combining like terms on right

10x + 5y = 8x + 3y + c

Subtracting 8x and 3y to solve for c

2x + 2y = c

The third side of the triangle is 2x + 2y.

To check: Add all sides of the triangle to see if you get the proper sum.

Does 3x + 4y + 5x - y + 2x + 2y equal 10x + 5y ?

3x + 5x + 2x = 10x

4y - y + 2y = 5y Yes! 10x + 5y = 10x + 5y