Rhombus from area and one diagonal The area of a rhombus is 84 cm² and one diagonal measures 7 cm. Find the length of the other diagonal (in cm).

Introduction / Context:For a rhombus, area equals half the product of its diagonals. Thus, knowing the area and one diagonal allows us to directly compute the other diagonal using a simple algebraic rearrangement.

Given Data / Assumptions:

• Area A = 84 cm²
• One diagonal d1 = 7 cm
• Unknown diagonal d2

Concept / Approach:Use A = (d1 * d2) / 2 ⇒ d2 = 2A / d1. Substitute the values to find d2 exactly.

Step-by-Step Solution:

Verification / Alternative check:Check: (7 * 24)/2 = 84 cm², which matches the given area perfectly.

Why Other Options Are Wrong:12 and 36 halve or 1.5x the correct value; 48 doubles the right answer; only 24 satisfies A = (d1 * d2)/2.

Common Pitfalls:Confusing the rhombus area with the parallelogram area (b * h) is unnecessary here; the diagonal formula is the direct route.

Final Answer:24