Question

A rectangle with one side equal to $6cm$ is inscribed in a circle of radius $5cm$. Then the area of the rectangle is

• A. $36c{m}^2$
• B. $42c{m}^2$
• C. $48c{m}^2$
• D. $54c{m}^2$

Answer 1

The correct option is C $48c{m}^2$

Given that, a rectangle with one side equal to $6cm$ is inscribed in a circle of radius $5cm$.

Let, the length of side $CD=6cm$.

Diameter of circle =Diagonal of rectangle $=BD=10cm$.

In $\Delta DBC$,

$B{D}^2=C{D}^2+C{B}^2$

$\Rightarrow {10}^2=6^2+C{B}^2$

$\Rightarrow C{B}^2=64$

$\Rightarrow CB=8$

Now,Area of rectangle $=l\times b=8\times 6=48c{m}^2$

Hence, this is the answer.