Question
Two paths of width 5 metres are to be made in the centre
of rectangular field such that they are perpendicular to each other. Find the area (in m2) of the field left after making the path if A can complete a round of the field along its boundary in 10.4 seconds while travelling with a speed of 5 m/s and difference between length and breadth of the field is 5 metres.Solution
Let length of the field is ‘l’ metres Breadth of the field = ‘l – 5’ metres So, 2 × (l + l – 5) = 10.4 × 5 = 52 So, 2l – 5 = 26 Or, 2l = 31 So, l = 15.5 metres And b = 15.5 – 5 = 10.5 metres Desired area = 15.5 × 10.5 – {15.5 × 5 + 10.5 × 5 – 5 × 5} = 162.75 – 105 = 57.75 m2
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