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# The diagonal of the floor of a rectangular closet is 7 1/2 feet. The shorter side of the closet is 4 1/2 feet. What is the area of the closet in square feet?

Option :

Explanation:

Solution:
$\begin{array}{rl}& \text{Outer}\phantom{\rule{thinmathspace}{0ex}}\text{Side}\\ & =\sqrt{{\left(\frac{15}{2}\right)}^{2}-{\left(\frac{9}{2}\right)}^{2}}ft\\ & =\sqrt{\frac{225}{4}-\frac{81}{4}ft}\\ & =\sqrt{\frac{144}{4}ft}\\ & =6ft\\ & \therefore \text{Area}\phantom{\rule{thinmathspace}{0ex}}\text{of}\phantom{\rule{thinmathspace}{0ex}}\text{closet}=\left(6×4.5\right)sq.\phantom{\rule{thinmathspace}{0ex}}ft=27\phantom{\rule{thinmathspace}{0ex}}sq.\phantom{\rule{thinmathspace}{0ex}}ft.\end{array}$