A rhombus has diagonals 24 cm and 10 cm. Find the area (in sq cm) and the perimeter (in cm) of the rhombus, respectively, using standard rhombus diagonal properties.

Introduction / Context: This problem checks two core rhombus facts: (1) Area can be found directly from diagonals using Area = (d1*d2)/2, and (2) diagonals bisect each other at right angles, allowing side length to be found by the Pythagoras theorem using half-diagonals. Once the side is known, perimeter is 4 times the side. The main goal is to produce the correct ordered pair: (area, perimeter).

Given Data / Assumptions:

• d1 = 24 cm
• d2 = 10 cm
• Area = (d1*d2)/2
• Half diagonals: 12 cm and 5 cm
• Side s = sqrt(12^2 + 5^2)

Concept / Approach: Compute area using diagonals formula. Compute side using right triangle formed by half diagonals. Then perimeter = 4*s. Keep units consistent (sq cm for area, cm for perimeter).

Step-by-Step Solution:Area = (d1*d2)/2 = (24*10)/2 = 240/2 = 120 sq cmHalf diagonals are 12 cm and 5 cmSide s = sqrt(12^2 + 5^2) = sqrt(144 + 25) = sqrt(169) = 13 cmPerimeter = 4*s = 4*13 = 52 cm

Verification / Alternative check: Since 12-5-13 is an exact Pythagorean triple, side = 13 is exact. Also area calculation is direct and exact. Therefore the ordered result (120, 52) is consistent and does not require rounding.

Why Other Options Are Wrong: Area 240 doubles the correct area because the division by 2 was missed. Perimeter 48 or 50 uses an incorrect side length due to not halving diagonals or incorrect square root. Area 110 or 130 indicates arithmetic mistakes in 24*10/2.

Common Pitfalls: Forgetting Area = (d1*d2)/2. Not halving diagonals before Pythagoras. Mixing up units (writing cm for area). Giving only one value when the question asks for both in order.

Final Answer: Area 120 sq cm, Perimeter 52 cm