One diagonal of a rhombus is twice as long as the other diagonal. If the rhombus has area 128 cm², find the length of the shorter diagonal.

Step-by-step solution

Idea: The diagonals of a rhombus cut each other at right angles, so its area is half the product of the diagonals.

1. Let the shorter diagonal be d; the longer is 2d. Area = 12 × d × 2d = d².1 mark
2. d² = 128 ⇒ d = √128 = √(64 × 2) = 8√2 ≈ 11.31 cm.1 mark

Check: Diagonals 8√2 and 16√2: 12 × 8√2 × 16√2 = 12 × 256 = 128 ✓.

Answer to write in the exam

Common mistakes that cost marks

• Writing area = d × 2d (forgetting the 12), giving d = 8.
• Giving the longer diagonal (16√2) instead of the shorter one.

How this can come in the exam

Try one yourself

One diagonal of a rhombus is three times the other, and its area is 150 cm². Find the diagonals.

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