Question

PQRS is a rectangle inscribed in a quadrant of a circle of radius 13 cm. A is any point on PQ. If $PS=5$ cm, Find $A\left(\Delta PAS\right)$.

• A. $30c{m}^2$
• B. $25c{m}^2$
• C. $24c{m}^2$
• D. $32c{m}^2$

Answer 1

The correct option is A $30c{m}^2$

Given-

PQRS is a rectangle inscribed in the quadrant of a circle of radius 13cm. i.e $SQ=13$cm.

Also $PS=5$cm.

A is any point on PQ.

To find out-

The staement $A\left(\Delta PAS\right)={30cm}^2$ is true or false

Solution-

PQRS is a rectangle with diagonal $SQ=13$cm.

$\therefore {SP}^2+{PQ}^2={SQ}^2$

$⟹PQ=\sqrt{{PQ}^2-{SP}^2}$

$⟹PQ=\sqrt{{13}^2-5^2}cm=12$cm

$\therefore A\left(\Delta PAS\right)=\frac{1}{2}\times SP\times PA=\frac{1}{2}\times 5\times PA=2.5PA$

Now, A is a point on PQ

$\therefore PA\le$ or $>\frac{1}{2}PQ$

$\therefore A\left(\Delta PAS\right)=2.5PQ\le$ or $>2.5\times \frac{1}{2}12{cm}^2\le$ or $>15{cm}^2$

So, $A\left(\Delta PAS\right)$ may or may not be $=30{cm}^2$