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In a rhombus whose area is 144 sq.cm on of its diagonals is twice as long as the other. The lengths of its diagonals are:_________?

Correct answer: B. 12cm,24cm

  • A. 24 cm,48cm
  • B. 12cm,24cm
  • C. 6√2cm,12√2cm
  • D. 6cm,12cm

Explanation

The area of a rhombus is half the product of its diagonals. Let the shorter diagonal be d centimetres, so the longer one is 2d centimetres; then 144 square centimetres = (d × 2d) ÷ 2 = d² square centimetres. Therefore d = 12 centimetres and the diagonals are 12 centimetres and 24 centimetres. The likely mistake is choosing 24 centimetres and 48 centimetres, which gives an area of 576 square centimetres, not 144 square centimetres.

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