Question
The perimeter of a rectangular field is 80 metres and
its area is 187.5 m2 . What is the length of the diagonal of this field?Solution
Let the length and breadth of the rectangular field be ‘p’ metres and ‘q’ metres respectively Then, according to the question, 2 × (p + q) = 80 Or, (p + q) = 80/2 = 40…… (1) Also p × q = 187.5 We know, (p + q)2 = p2 + q2 + 2pq Or, p2 + q2 = 402 – 2 × 187.5 Or, p2 + q2 = 1225 So, length of the diagonal of the rectangular field = √(length2 + breadth2) = √(p2 + q2) = √1225 = 35 metres
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