A rectangular patio is 8 feet longer than it isi wide The area of the patio is 84 square feet. What are the dimensions of the patio

Is it x=6

6 feet is the width. What is the length?

14 Right.

To find the dimensions of the patio, let's solve this problem step by step.

Let's assume the width of the patio is "x" feet.
According to the given information, the length of the patio is 8 feet longer than its width. So, the length would be "x + 8" feet.

The formula for the area of a rectangle is length multiplied by width. In this case, we have the area given as 84 square feet.

Therefore, the equation for the area of the patio is: x(x + 8) = 84.

Now, let's solve this equation using the distributive property:

x^2 + 8x = 84.

Rearranging the equation:

x^2 + 8x - 84 = 0.

Now we need to factorize this equation to find the values of "x" that satisfy this equation:

(x + 14)(x - 6) = 0.

So, we have two possible solutions for "x":
1) x + 14 = 0 --> x = -14 (not a valid solution in this context).
2) x - 6 = 0 --> x = 6.

Since the width cannot be negative, the width of the patio is 6 feet.
Now we can find the length by adding 8 to the width:

Length = 6 + 8 = 14 feet.

Therefore, the dimensions of the patio are 6 feet wide and 14 feet long.