Question

the basement has an area of 864 square feet. the width of the basement is two thirds its length. What is the length of the basement?

Answer 1

$Area=Length*Width \\ A=LW \\ 864=( \frac{2}{3}L )L \\ 864= \frac{2}{3}L^{2} \\ 1296=L^{2} \\ L= \sqrt{1296} \\ \boxed{Length=36\ feet}$

Answer 2

A = 864
w = 2/3l

A = lw

Plug in what we know:

864 = l(2/3l)

Multiply:

864 = 2/3l^2

Divide 2/3 to both sides or multiply by its reciprocal, 3/2:

864 * 3/2 = l^2

2592/2 = l^2

1296 = l^2

Find the square root of both sides:

l = 36

So the length of the basement is 36 feet.