Question

The length of a rectangle is 4ft less than its width.The area of the rectangle is 6oft
`^(2)`. find the length and width of the rectangle

Answer 1

Width is 10ft and length is 6ft.

Explanation:

The area of a shape is the amount inside a shape. It is found using multiplication or A = l*w. Since the width is w and the length is 4ft less than its width or w - 4, use these expressions in the area formula to find their amount.

`A = l*w\\60 = w(w -4)\\60 = w^2-4w`

Subtract 60 from both sides and factor the quadratic to solve for w.

`w^2 -4w - 60 = 0\\(w-10)(w+6) = 0`

Set each factor equal to 0 and solve.

w - 10 = 0 so w = 10

w + 6 = 0 so w = -6.

Since w represents a length or distance it cannot be negative, this means the width is 10. The length which is w - 4ft is 10 -4 = 6. The length is 6 ft.