# The perimeter of a rectangular outdoor patio is 60 ft. The length is 4 ft greater than the width....

## Question:

The perimeter of a rectangular outdoor patio is 60 ft. The length is 4 ft greater than the width. What are the dimensions of the patio?

## Perimeter of a Rectangle:

The formula for the perimeter of a rectangle of length {eq}l {/eq} and width {eq}w {/eq} is given by:

$$\text{Perimeter } = 2 l +2 w$$

If we know the length and width of a rectangle in terms of a variable and its perimeter is given then we can substitute all the values in the above formula and solve for the variable.

Let us assume the width of the rectangular outdoor patio be {eq}w=x {/eq} ft.

The problem says, "The length is 4 ft greater than the width".

So we get its length to be {eq}l= x+4 {/eq}.

Its perimeter is given to be {eq}60 {/eq} ft.

We substitute all these values in the perimeter of a rectangle formula:

$$\text{Perimeter } = 2 l +2 w \\[0.4cm] 60= 2 (x+4)+2x \\[0.4cm] \text{Distributing 2},\\[0.4cm] 60=2x+8+2x\\[0.4cm] \text{Combining the like terms}, \\[0.4cm] 60=4x+8 \\[0.4cm] \text{Subtracting 8 from both sides}, \\[0.4cm] 52=4x \\[0.4cm] \text{Dividing both sides by 4}, \\[0.4cm] 13 =x$$

Therefore, the width of the rectangular outdoor patio is, {eq}x= \boxed{\mathbf{13 \text{ ft}}} {/eq}

and its length is, {eq}x+4= 13+4 = \boxed{\mathbf{17 \text{ ft}}} {/eq}. 