Question

A rectangle's length is 4 feet more than it's width. If the area of the rectangle is 396 square feet, what is its width, in feet?

Answer 1

Area of a rectangle = L × W
Let the width be x
Then, the length = 4x
396 = 4x × x
396 = 4x^2
Divide both sides by 4
396/4 = 4x^2/4
99 = x^2
Take the square root of both sides

`√(99 ) = \sqrt{} {x}^(2)`
x = 9.9499

Answer 2

18 feet

Explanation:

Let the width of the rectangle to be x.

Therefore, the length which is 4 feet more than the width will be = x + 4

We know that the Area of a rectangle = L x W, so we will substitute the values of area, length and width in it to get:

Area = L x W

396 = (x + 4) (x)

396 = x^2 + 4x

x^2 + 4x - 396 = 0

Now we will factorize this quadratic equation:

x^2 + 4x - 396 = 0

x^2 + 22x - 18x -396 = 0

x (x + 22) - 18 (x + 22) = 0

x = -22 (ignore) and x = 18

So width is 18 feet and by adding 4 to it we can know the length which is 18 + 4 = 22 feet.