The perimeter of a rectangular field is 42 metres and its area is 108 m2 . What is the length of the diagonal of this field?
Let the length and breadth of the rectangular field be ‘p’ metres and ‘q’ metres respectively Then, according to the question, 2 × (p + q) = 42 Or, (p + q) = 42/2 = 21…… (1) Also p × q = 108 We know, (p + q)2 = p2 + q2 + 2pq Or, p2 + q2 = 212 – 2 × 108 Or, p2 + q2 =441-216=225 So, length of the diagonal of the rectangular field = √(length2 + breadth2) = √(p2 + q2) = √225 = 15metres
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