The diagonals of a rhombus are 32 cm and 24 cm. Its perimeter will be

The correct answer is D. The diagonals of a rhombus bisect each other at right angles, so each half-diagonal is 16 cm and 12 cm. These halves, together with one side, form a right-angled triangle. By Pythagoras, side² = 16² + 12² = 256 + 144 = 400, so each side is 20 cm. All four sides are equal, so the perimeter is 4 × 20 = 80 cm.

The other options do not follow from this relation. A side of 12.5 cm (for 50 cm), 15 cm (for 60 cm) or 17.5 cm (for 70 cm) would need half-diagonal squares that sum to 156, 225 or 306.25, and 16² + 12² is 400.

The core concept is the property that a rhombus's diagonals bisect each other at right angles, combined with Pythagoras. This kind of quadrilateral-geometry reasoning is standard in the mensuration and geometry portions of the General Studies and aptitude papers.

Trap: Using the full diagonals (32 and 24) instead of their halves in Pythagoras gives a side of 40 cm, and multiplying the side by 2 instead of 4 for the perimeter gives a wrong value. Always halve the diagonals first and multiply the side by four.