Question 156964
The perimeter of a rectangular garden is 24 ft. The length is 2 ft more than the width. Find the length and the width of the garden.

We need the perimeter of a rectangle formula: P = 2L + 2W

Let P = 24

length = x + 2

width = x

Plug into above formula and solve for x.

24 = 2(x + 2) + 2x

We need to distribute 2 across the quantity (x + 2) to remove the parentheses.

Let's do that first.

2 times x = 2x

2 times 2 = 4

This is our new equation:

24 = 2x + 4 + 2x

Combining like terms on the right side we get:

24 = 4x + 4

Subtracting 4 from both sides of the equation, we get this:

24 - 4 = 4x

20 = 4x

To find x, we use the division property of equality that tells us to divide both sides by the number next to x on both sides. So, this means we divide both sides by 4 to find the value of x.

20/4 = x

5 = x

We just found x to be 5.

However, we need to find the length and width.

Our length is x + 2

Replace x with 5 and add 2.

Length = 5 + 2

Length = 7 feet

Our width is W.

Replace W with 5.

Our width is 5 feet.

Done!