Question

Assertion (A): The perimeter of the adjoining figure is (32 + x) cm.

Reason (R): x² = 13² − 5² = 144 and x = 12 cm Perimeter = (32 + 12) cm.

Options

• 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

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

Explanation:

The perimeter is the sum of all outer boundary lengths (\[x + 12 + 13 + 7 = x + 32\]), making Assertion A true. Reason R correctly applies the Pythagorean theorem to find the missing base segment \[x = \sqrt{13^2 - 5^2} = 12\text{ cm}\], making it the correct explanation.