Question

Question 2
Write True or False and justify your answer :
PQRS is a rectangle inscribed in a quadrant of a circle of radius 13 cm and A is any point on PQ. If PS = 5 cm. Then, ar ($\Delta$PAS)= $30c{m}^2$.

Answer 1

Given, PS = 5 cm
Radius of the circle = SQ = 13 cm

In right angled $\Delta$ SPQ, $S{Q}^2=P{Q}^2+P{S}^2$ [by Pythagoras theorm]
$(13{)}^2=P{Q}^2+(5{)}^2$
$\Rightarrow P{Q}^2=169-25=144$
$\Rightarrow PQ=12cm$
[taking positive square root, because length is always positive]
Now, area of $\Delta APS=\frac{1}{2}\times Base\times Height$
$\frac{1}{2}\times 5\times 12=30c{m}^2$
So, given statement is true, if A coincides Q.