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The diagonal of the floor of a rectangular room is $MF#%7\dfrac{1}{2}$MF#% feet. The shorter side of the room is 4 $MF#%\dfrac{1}{2}$MF#% feet. What is the area of the room?
Options:
A .  27 square feet
B .  22 square feet
C .  24 square feet
D .  20 square feet
Answer: Option A

Answer : Option A

Explanation :

The Diagonal Of The Floor Of A Rectangular Room Is $MF#%7\df...

$MF#%\begin{align}
&\text{Diagonal, d = 7}\dfrac{1}{2}\text{ feet } = \dfrac{15}{2}\text{ feet}\\
&\text{Breadth, b = 4}\dfrac{1}{2}\text{ feet} = \dfrac{9}{2}\text{ feet}\\\\\\\\
&\text{In the right-angled triangle PQR,}\\
&l^2 = \left(\dfrac{15}{2}\right)^2 - \left(\dfrac{9}{2}\right)^2 \\\\
&= \dfrac{225}{4} - \dfrac{81}{4} = \dfrac{144}{4}\\\\
&l = \sqrt{\dfrac{144}{4}} = \dfrac{12}{2}\text{ feet = 6 feet}\\\\\\\\\\
&\text{Area = lb = }6 \times \dfrac{9}{2} = 27 \text{ feet}^2
\end{align} $MF#%



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