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.

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.

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
                   

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