Question 184

The ratio between the length and the breadth of a rectangular park is 3:2. If a man cycling along the boundary of the park at the speed of 12 kmph completes one round in 8 minutes, then the area of the park is equal to

Solution

Let length of the park = $$3x$$ metre and breadth = $$2x$$ metre

Now, perimeter of the park = distance covered by the cyclist in one round

= $$\frac{12*8}{60} = \frac{8}{5} km$$ = 1600 $$m$$

According to question,

=> 2 * $$(3x + 2x)$$ = 1600

=> $$x$$ = 160

=> Area of the park = $$3x * 2x$$ = $$6x^2$$

= 6 * 160 * 160 = 153600 $$m^2$$

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