Question

A square has a side length of x inches. Each side of the square will be increased by 8 inches to create a larger square. If the larger square has a perimeter of 40 inches, what is the side length, in
inches of the original square?

Answer 1

X = 2

A square has 4 sides. To get the perimeter of a square, you could multiply the length of one side by 4.

One side of the larger triangle is x inches plus an additional 8 inches, which can be written as (x+8)

To get the perimeter of the larger square, multiply the expression (x+8) by 4. The question states the larger square’s perimeter is 40 inches.

You end up with this equation: 4(x + 8) = 40

To solve first distribution 4 into (x + 8).
4x + 32 = 40 | subtract 32 from both sides
4x = 8 | divide each side by 4
x = 2 inches

So the side length of the original square is 2 inches. To check your work, go back and plug x = 2 into the original equation. 8 in + 2 in = 10 inches, and 10 inches x 4 = 40 inches, so x = 2 is the solution