Question
The perimeter of a rectangular field is 70 metres and
its area is 100.5 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) = 70 Or, (p + q) = 70/2 = 35…… (1) Also p × q = 100.5 We know, (p + q)2 = p2 + q2 + 2pq Or, p2 + q2 = 352 – 2 × 100.5 Or, p2 + q2 = 1024 So, length of the diagonal of the rectangular field = √(length2 + breadth2) = √(p2 + q2) = √1024 = 32 metres
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