Rhombus area 144 sq cm, diagonals in 1:2 ratio — find the diagonals: A rhombus has area 144 sq cm. One diagonal is twice the other. Find the lengths of both diagonals.

Introduction / Context:
Area of a rhombus equals half the product of its diagonals. A given ratio allows solving each diagonal explicitly.

Given Data / Assumptions:

• Area = 144 sq cm
• Let shorter diagonal = d, longer diagonal = 2d

Concept / Approach:
Use A = (d * 2d)/2 = d^2. Therefore d = sqrt(144) = 12, so the longer diagonal is 24.

Step-by-Step Solution:
A = d^2 ⇒ d = 12 cmLonger diagonal = 2d = 24 cm

Verification / Alternative check:
Check: (12 * 24)/2 = 144 ✓

Why Other Options Are Wrong:
24, 48 doubles area; options with √2 are for squares via side relations, not diagonal ratio given here; 6, 12 halves the correct values.

Common Pitfalls:
Taking the square root incorrectly or mixing which diagonal is longer.

Final Answer:
12 cm, 24 cm