Question

The width of a rectangle is 8 less than twice its length. if the area of the rectangle is 137 cm^2, what is the length of the diagonal?

Answer 1

Length (L): L

width (w): 2L - 8

Area (A) = L x w

137 = L(2L - 8)

137 = 2L² - 8L

0 = 2L² - 8L - 137

L =
`[-(-8) +/- \sqrt{(-8)^(2)  - 4(2)(-137) }]/2(2)`

=
`[8 +/- √((64  + 1096 )]/4`

=
`[8 +/- √((1160 )]/4`

=
`[8 +/- 2√((290 )]/4`

=
`[4 +/- √((290 )]/2`

since length cannot be negative, disregard [4 - √290]/2

L = [4 + √290]/2 = 10.51

width (w): 2L - 8 = 2(10.51) - 8 = 21.02 - 8 = 13.02

Answer: width = 13.02 cm, length = 10.51 cm