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.

Question

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.

Answer 1

False. Since A is any point on PQ, then ar (PAS) ≠ 30 cm²

But, the statement can be true if PA is equal to PS.

Justification:

According to the question,

PQRS is a rectangle inscribed in a quadrant of a circle of radius 13 cm.

Given,

A is any point on PQ

PA<PQ

ar (△PQR) = ½ × PQ × QR

= ½ × 12 × 5

= 30 cm²

PS = 5 cm

Suppose PA<PQ,

ar(△PAS) < ar(△PQR)

ar(△PAS) < 30 cm²

Suppose PA = PQ,

ar (△PAS) = ½ × PQ × PS

= ½  × 12 × 5

= 30 cm²