Question

The area of a rectangle is 27 square meters. If the length is 6 meters less than 3 times the width, then find the dimensions of the rectangle. Round off your answers to the nearest hundredth.

Answer 1

Length (L): 3w - 6

width (w): w

Area (A) = L x w

27 = (3w - 6)w

27 = 3w² - 6w

0 = 3w² - 6w - 27

0 = 3(w² - 2w - 9)

w =
`[-(-2) +/- \sqrt{(-2)^(2)  - 4(1)(-9) }]/2(1)`

=
`[2 +/- √((4  + 36 )]/2`

=
`[2 +/- √((40 )]/2`

=
`[2 +/- 2√((10 )]/2`

=
`[1 +/- √((10 )]`

since width cannot be negative, disregard 1 - √10

w = 1 + √10 = 4.16

Length (L): 3w - 6 = 3(4.16) - 6 = 12.48 - 6 = 6.48

Answer: width=4.16 meters, length=6.48 meters