Question
The perimeter of a rectangular field is 44 metres and its area is 114 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) = 44 Or, (p + q) = 44/2 = 22…… (1) Also p × q = 114 We know, (p + q)2 = p2 + q2 + 2pq Or, p2 + q2 = 222 – 2 × 114 Or, p2 + q2 = 256 So, length of the diagonal of the rectangular field = √(length2 + breadth2) = √(p2 + q2) = √256 = 16 metres
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