Question 30

A rectangular plot 55 m long and 45 m broad, has two concrete crossroads (of equal width) running in the middle of it - one parallel to the length and the other parallel to the breadth. The rest of the plot is used as a lawn. If the area of the lawn is 1911 m2, what is the width of each of the crossroads ? (in m)

Solution

Let w be the width of the crossroads.
Area of the one shaded portion = [(55-w)/2][(45-w)/2]
Area of the entire shaded portion = 4 $$\times$$ Area of the one shaded portion = (55-w)(45-w) = 2475-55w-45w+w $$^2$$
Given Area of lawn(shaded portion) = 1911 m $$^2$$
2475-55w-45w+w$$^2$$ = 1911
w$$^2$$ -100w + 564 = 0
Solving for w, we get w=6 and w=94.
w=6 is the only possible answer.
Hence Option C is the correct answer.