Find the dimensions of the rectangle

Question

The length of a rectangle is 9 centimeters less than four times its width. Its area is 28 square centimeters.

Answer 1

Hi Megi,

 

We can find the dimensions of the rectangle using the area formula:

    w = width (in cm)

    l = 4w - 9 (9 cm less than 4 times width)

    Area = length x width

    28 = (4w - 9)(w)

    28 = 4w² - 9w

    4w² - 9w - 28 = 0

    4w² + (-16 + 7)w - 28 = 0

    4w² - 16w + 7w - 28 = 0

    4w(w - 4) + 7(4w - 4) = 0

    (4w + 7)(w - 4) = 0

    4w + 7 = 0  |   w - 4 = 0

    4w = -7       |   w = 4 cm (width)

    w = -(7/4) (reject negative answer)

    l = 4w - 9 

    l = 4(4) - 9

    l = 16 - 9

    l = 7 cm (length)

 

We can verify these dimensions by plugging them back into the area formula and see if they yield our given area:

    area = length x width (l = 7; w = 4)

    28 = 7 x 4

    28 = 28 (dimensions are correct)

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.