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.

Answer and Explanation:

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}.