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  • Write true or false and justify your answer. 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,then ar (PAS) = 30 cm^2.

Write true or false and justify your answer.
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,then ar (PAS) = 30 cm2.

Answers (1)

best_answer

Answer: [False]

Solution.

It is given that PQRS is a rectangle inscribed in a quadrant of a circle of radius 13 cm.
A is any point on PQ, therefore, PA < PQ.
It is given that A is any point on PQ, therefore PA < PQ.

PS = 5 cm, PR = 13 cm
In DPSR, using Pythagoras theorem,
PS^{2}+SR^{2}=PR^{2}
5^{2}+SR^{2}=13^{2}
SR^{2}=169-25=144
SR = 12 cm = PQ (opposite sides of a rectangle are equal)
Area of a triangle is given as  \frac{1}{2}\times base\times height
Now,  ar(\triangle PQR)=\frac{1}{2}\times PQ\times QR =\frac{1}{2}\times 12\times 5=30cm^{2}
As, PA< PQ

ar(\triangle PAS)<ar(\triangle PQR)
or   ar(\triangle PAS)<30cm^{2}
But it is given that  ar( PAS)=30cm^{2}

Hence, the given statement is false.

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