Question

The width of a rectangle is 4 inches less than its length. The area of the rectangle is 45 square inches. What is the length of the rectangle?

A. 4 inches
B. 5 inches
C. 9 inches
D. 14 inches

Answer 1

The formula of an area of a rectangle:

`A=lw`

l - length

w - width

We have w = l - 4 and A = 45 in²

Therefore we have the equation:

`l(l-4)=45` use distributive property

`l^2-4l=45` subtract 45 from both sides

`l^2-4l-45=0\\\\l^2+5l-9l-45=0\\\\l(l+5)-9(l+5)=0\\\\(l+5)(l-9)=0\iff l+5=0\ \vee\ l-9=0\\\\l=-5 < 0\ \vee\ \boxed{l=9}`

Answer: C. 9 inches