Question

A rectangle with one side equal to 4 cm is inscribed in a circle of diameter 5 cm. Then the area of the rectangle is

• A. $12c{m}^2$
• B. $15c{m}^2$
• C. $16c{m}^2$
• D. $8\sqrt{2}c{m}^2$

Answer 1

The correct option is A $12c{m}^2$

Let the breadth of the rectangle be $b$.

The length of rectangle be $l=4cm$

Since, the diameter of the circle $=5cm$

By using Pythagoras theorem,

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

$5^2=l^2+b^2$

$25=4^2+b^2$

$b=3cm$

Therefore, the area of the rectangle will be

$=l\times b$

$=4\times 3=12c{m}^2$

Hence, this is the answer.