Find the Iength of a diagonal of a square whose area is 288cm2.

Analyze the question: We're given the area of a square (288 cm²) and need the length of its diagonal.

Concept: For a square with side s:

• Area = s²
• Diagonal d = s√2
• So the area can be written as A = d²/2, which means d² = 2A.

Solution:

Using d² = 2 × Area:

d² = 2 × 288 = 576

d = √576 = 24 cm

Check using the side length: s² = 288, so s = √288 = 12√2 d = s√2 = 12√2 × √2 = 12 × 2 = 24 cm ✓

Answer: The diagonal is 24 cm, which is option A.

Tip: For any square, remember d² = 2 × Area. You can skip finding the side entirely. Here 2 × 288 = 576, and 576 is a perfect square (24²). Learning common perfect squares like 576 saves time in the exam hall.