Question

The diagonal of the floor of a rectangular closet is $5$ metres. The shorter side of the closet is $3$ metres. What is the area of the closet in square metres?

• A. $15$
• B. $12.5$
• C. $12$
• D. $10$

Answer 1

The correct option is C $12$

Let the closet be $ABCD$
Diagonal $AC=BD=5$ m
Shorter side $AD=BC=3$ m
To find the longer side, we will apply pythagoras theorem
In $\Delta ADB$, we have
$A{B}^2+A{D}^2=B{D}^2$
$\Rightarrow A{B}^2=5^2-3^2$
$\Rightarrow A{B}^2=16$
$\Rightarrow AB=4$ m
Now, Area of closet $ABCD=L\times B$
$=3\times 4$
So, area of closet $=12$ sq.m.