The formula for the perimeter is P = 2<em>w</em> + 2<em>l</em>, where <em>w</em> is the width and <em>l</em> is the length. It is given that the width = (x+2) and the length = (x+6). Therefore, we can make this equation:
P = 2<em>w</em> + 2<em>l</em>
64 = 2(x+2) + 2(x+6) ⇒ Distributive property
⇒ 64 = 2x + 4 + 2x + 12 ⇒ Combine like terms
⇒ 64 = 4x + 16 ⇒ Subtract 16 from both sides
⇒ 48 = 4x ⇒ Divide both sides by 4
⇒ x = 12
Then, we use x = 12 and substitute it in to find the length and width
<em>Width</em> = (x+2) = (12+2) = 14
<em>Length</em> = (x+6) = (12+6) = 18
The dimensions of the patio is <u>14 by 18</u>
