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Let the length and breadth of the rectangular field be ‘p’ metres and ‘q’ metres respectively Then, according to the question, 2 × (p + q) = 22 Or, (p + q) = 22/2 = 11…… (1) Also p × q = 20 We know, (p + q)2 = p2 + q2 + 2pq Or, p2 + q2 = 112 – 2 × 20 Or, p2 + q2 = 81 So, length of the diagonal of the rectangular field = √(length2 + breadth2) = √(p2 + q2) = √81 = 9 metres
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