A rhombus has diagonals of lengths 24 cm and 10 cm. Using these diagonals, find the perimeter of the rhombus in centimetres (cm).

Introduction / Context:
This question tests properties of a rhombus: its diagonals bisect each other at right angles. If you know the diagonals, you can find the side length by forming a right triangle using half of each diagonal. Once a single side is known, the perimeter is simply 4 times the side length. The core idea is converting diagonal information into side length via the Pythagoras theorem.

Given Data / Assumptions:

• Diagonal 1 = 24 cm
• Diagonal 2 = 10 cm
• Diagonals bisect each other at right angles
• Half diagonals are 12 cm and 5 cm

Concept / Approach:
In a rhombus, each side is the hypotenuse of a right triangle whose legs are half of the diagonals. So side s = sqrt((d1/2)^2 + (d2/2)^2). Then perimeter P = 4*s.

Step-by-Step Solution:
Half of 24 cm = 12 cmHalf of 10 cm = 5 cmSide s = sqrt(12^2 + 5^2)s = sqrt(144 + 25) = sqrt(169) = 13 cmPerimeter P = 4*s = 4*13 = 52 cm

Verification / Alternative check:
Because 12-5-13 is a well-known Pythagorean triple, the side length 13 is exact and not approximate. Perimeter then must be 4*13 = 52. This makes the answer highly reliable.

Why Other Options Are Wrong:
56 and 48 typically come from small arithmetic mistakes or using 14 or 12 as the side incorrectly. 68 and 72 happen if someone mistakenly adds diagonal lengths or uses full diagonals instead of halves inside the square root.

Common Pitfalls:
Forgetting to halve the diagonals. Not using the right-angle property at the intersection of diagonals. Computing area instead of perimeter. Rounding unnecessarily even though the result is exact (13).

Final Answer:
52 cm