Question
A rectangular field has a perimeter of 82 meters, and
the length of its diagonal measures 29 meters. Determine the area of the field.Solution
Let the length and breadth of the rectangular field be 'l' metres and 'b' metres, respectively. Then, perimeter of the field = 2 X (l + b) = 82 So, (l + b) = 82 ÷ 2 = 41 (l + b)2 = l2 + b2 + 2lb = 1681 Also, l2 + b2 = 292 = 841 So, 2lb = 1681 - 841 = 840 So, lb = 840 ÷ 2 = 420 m2
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