Question

In the fig., OABC is a rectangle inscribed in a quadrant of a circle of radius 25cm. Find the area of the rectangle if OC =7cm.

Answer 1

Diagonal of rectangle = 25 cm (radius). Another side^2 = 25^2 - 7^2 = (25 + 7)(25 - 7) = 32 x 18 = 576 OR, side = root 576 = 24 cm Hence, area = 24 x 7 = 168 sq cm

Answer 2

Answer:

The area of rectangle is 168 cm².

Step-by-step explanation:

The radius of the circle is 25 cm. It means OB is 25 cm.

It is given that OABC is a rectangle it means triangle OBC is a right angled triangle.

Using Pythagoras theorem,

$OB^2=OC^2+CB^2$

$25^2=7^2+CB^2$

$625-49=CB^2$

$576=CB^2$

$CB=24$

The length of the rectangle is 24 cm.

The area of rectangle is

$A=length \times width$

$A=24\times 7=168$

Therefore the area of rectangle is 168 cm².