Question

The length of a rectangular room is one less than twice the width. The area of the room is 28 square feet. Find the dimensions of the room.

Answer 1

The first step to solve this problem is to represent variables for the width and the length:

Let w = width of the rectangle

      2w – 1 = length of the rectangle

The formula to compute for the area of the rectangle is:

A = LW

Substituting the values and variables to the formula:

28 = w (2w – 1)

2w^2 – w = 28

2w^2 – w – 28 = 0

Solve the quadratic equation:

(2w + 7)(w – 4) = 0

w = -7/2 or w = 4

You cannot use the -7/2 because there is no negative measurement.

W = 4 feet

L = 2(4) – 1 = 7 feet

Therefore the dimension of the rectangle is 4 feet by 7 feet.

Answer 2

Equation: x(2x-1)=28

Create a quadratic equation: 2x^2 -x=28
                                              2x^2 -x-28=0

Find roots: plug into quadratic formula, x=4 or x=-7/2

Since x cannot be negative, x=4

Plug into original equation to find the width, width=7

Check: Plug into original equation or just multiply the two using the formula for area
            7*4=28
            28=28

Length is 4 ft, width is 7 feet