Question

Assertion (A): PQRS a parallelogram whose area is 180 cm² and A is any point on the diagonal PR. The area of triangle ASR = 45 cm².

Reason (R): A is not the mid-point of diagonal PR.

विकल्प

• A is true, R is false.

• A is false, R is true.

• Both A and R are true and R is the correct reason for A.

• Both A and R are true and R is the incorrect reason for A.

Answer 1

A is false, R is true.

Explaantion:

• Assertion (A): The diagonal PR divides the parallelogram PQRS into two triangles of equal area, meaning the area of ΔPSR is half the total area of the parallelogram:
  `\text{area of }\triangle PSR = \frac{1}{2} \times 180\text{ cm}^2 = 90\text{ cm}^2`
  Since point A lies on the diagonal PR, if A were the mid-point of PR, the median SA would divide ΔPSR into two equal parts of 45 cm² each. However, the problem states that A is any point on the diagonal PR, not specifically the mid-point. For an arbitrary point A on PR, the area of ΔASR is not guaranteed to be 45 cm² (as it depends on the exact position of A). Therefore, Assertion (A) is false.
• Reason (R): Since A is chosen as any point on the diagonal PR, it is not necessarily the mid-point of the diagonal, making Reason (R) true.