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CA Foundation · Quantitative Aptitude · Equations

A rectangular plot belonging to Mehta Farms has a perimeter of 34 metres and an area of 60 square metres. What is the length of its diagonal?

The sides satisfy x+y=17 and xy=60, giving a quadratic whose roots are 12 and 5. The diagonal is the square root of 144+25, which is 13 metres. The value 17 is only the sum of adjacent sides, not the diagonal length.

  1. A11 metres
  2. B12 metres
  3. C13 metresCorrect
  4. D17 metres

Explanation

Half the perimeter gives length + breadth = 17, and length × breadth = 60. So the sides are roots of t² − 17t + 60 = 0, i.e. (t − 12)(t − 5) = 0, giving 12 m and 5 m. The diagonal is √(144 + 25) = √169 = 13 m. The value 17 is only the sum of the two sides.

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