What is the value of x ?

Question

The triangle and the square have equal perimeters. 

1. Find the value of x.

Answer 1

To find the perimeter of a shape, you have to add up the length of each side.

So for the triangle, the perimeter would be:

(2x) + (2x) + (x-8) = 5x - 8

For the square we know that each side is the same length, so the perimeter would be:

(x+2) + (x+2) + (x+2) + (x+2) = 4x + 8

Now the problem tells us that the perimeter of the square is equal to the perimeter of the triangle, so we can set those 2 values equal to each other:

Triangle perimeter = Square perimeter

5x - 8 = 4x + 8

Now you just have to solve for x!

5x - 8 = 4x + 8

5x - 4x = 8 - (-8)

x = 8+8

x = 16

You can double check that the answer is correct by plugging 16 back into the equations you started with and see if you get an answer that makes sense:

(2*16) + (2*16) + (16-8) = 72

(16+2) + (16+2) + (16+2) + (16+2) = 72

I hope this helps!