Question

The area of a rectangle is 27 m^2 , and the length of the rectangle is 3 m less than twice the width. Find the dimensions of the rectangle.

Length: ___m
Width: ____m

Answer 1

Let
`L` be the length of the rectangle and
`W` be the width. In the problem it is given that
`L=2W-3`. It is also given that the area
`LW=27`. Substituting in the length in terms of width, we have
`W(2W-3)=27 \\ 2W^2-3W-27=0 \\ (2W-9)(W+3)=0`. Using the zero product property,
`2W-9=0 \text{ or } W+3=0`. Solving these we get the width
`W=4.5 \text{ or } -3`. However, it doesn't make sense for the width to be negative, so the width must be
`\boxed{4.5 \text{ m}}`. From that we can tell the length
`L=2(4.5)-3=\boxed{6 \text{ m}}`.