What is the value of X in the following question?

Question

The side lengths of a square are X - 3 and two side lengths of a triangle are X and one is 8, they both have the same perimeter.

Answer 1

Hi Evan,

Perimeter measures the distance around a shape or figure.

Using the expression (x-3) for the side of the square, its perimeter woudl be represented by 4 times that expression:

4(x-3)

For the triangle, the perimeter described would be sum the of the three side lengths or:

x + x + 8

Since both shapes have the same perimeter, we can write and solve the following equation to find the value of x:

4(x -3 ) = x + x + 8

Now use the distributive property, combining like terms ,and inverse operations to solve for x:

4x - 12 =2x + 8

4x -12 - 2x = 2x + 8 -2x

2x - 12= 8

2x - 12 + 12 = 8 + 12

2x = 20

2x/2= 20/2

x = 10

The value of x is 10.

The perimeter of the square will be 4(x-3) = 4(10 - 3) = 4(7) = 28

The perimeter of the triangle will be x + x + 8 = 10 + 10 + 8 =28