The central park of the city is 40 metres wide. The mayor wants to construct two roads of equal width in the park such that the roads intersect each other at right angles and the diagonals of the park are also the diagonals of the small rectangle formed at the intersection of the two roads. Further…

Question

The central park of the city is 40 metres wide. The mayor wants to construct two roads of equal width in the park such that the roads intersect each other at right angles and the diagonals of the park are also the diagonals of the small rectangle formed at the intersection of the two roads. Further, the mayor wants that the area of the two roads to be equal to the remaining area of the park. What should be the width of the roads?

Srikanth Lingamneni · Answer

Let the width of the roads be a.Area of each road = 40*aArea of the intersection = $$a^2$$Hence are of the roads = $$2*(40*a) - a^2$$ (subtracting the intersection area, as it is counted twice)From the problem, we have $$2(80a - a^2) = 40*40$$Solving the above equation we get a = $$20( 2 + 2\sqrt{2})$$

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