Question

Area of a rectangle is 100 sq ft. The length is 10 ft longer than twice it’s width. What is the length and the width.

Answer 1

The length of the rectange is 20ft and width of the 5ft.

Step-by-step explanation:

Let us consider a rectangle and its area is known to be 100 sq ft.

We are given the information that the length of the rectangle is 10ft longer than twice its width.

⇒Length l = 2w+10.

Where w is the width of the rectangle.

The formula for area of the rectangle A = length × width.

A= (2w+10)×w.

100 = $2w^2+10w$.

0=$2w^2+10w-100$.

Thus it forms an quadratic equation we have to solve for the solution.

0=(2w-10)(w+10).

2w-10=0.    w+10=0.

2w=10.        w=-10. (negative value cannot be choosed.)

w=$(\frac{10}{2} )$.        

w=5ft.

Thus width is is 5 ft.

Length = 2(5)+10.

=10+10.

=20ft.

Thus the length is 20ft.