Question

Assertion (A): In rhombus ABCD, angle ABC = 120° and length of its each side is 20 cm. The length of diagonal BD = 20 cm.

Reason (R): In ΔАОВ, cos 60° = `"OB"/"20 cm" and BD = 2 xx OB`.

पर्याय

• 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:

• In a rhombus, adjacent angles sum to 180°, so if ∠ABC = 120°, the angle bisector or half-angle at B for triangle AOB is 60°.
• Using the right triangle AOB, cos 60° = \[\frac{\text{OB}}{20}\], which gives \[\text{OB} = 20 \times \frac{1}{2} = 10\text{ cm}\].
• Since the diagonal \[\text{BD} = 2 \times\text{OB} = 2 \times 10 = 20\text{ cm}\], Assertion A is true and Reason R provides the exact correct trigonometric justification.