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 $L=2(4.5)-3=\boxed{6 \text{ m}}$.