Answer
Length is 15 inches; Width is 10 inches
Work Step by Step
The formula for the area of a rectangle is Area=Length x Width
You are given the ratio of length to width as 3:2. So, set the length equal to x, and solve for the width.
$\frac{3}{2}$=$\frac{x}{w}$
Cross Multiply
3w=2x
w=$\frac{2x}{3}$
You are given an area of 150 $in^{2}$, so substitute into the area formula.
A=LxW
150=x($\frac{2x}{3})$
150=$\frac{2x^{2}}{3}$
450=$2x^{2}$
225=$x^{2}$
15=x (this is the length; remember from above we let the length equal x.)
Use the proportion to solve for the width.
$\frac{l}{w}$=$\frac{3}{2}$
We know the length, so substitute it in for l:
$\frac{15}{w}$=$\frac{3}{2}$
Cross Multiply to get width:
3w=15(2)
3w=30
w=10
