Question

A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park, and the rest of the park is used as a lawn. If the area of the lawn is 2109 sq. m, what is the width of the road?

• A. 2.91 m
• B. 3 m
• C. 5.82 m
• D. None of these

Hint:

Road area = 60x + 40x - x^2 (subtracting the double-counted central overlap square); solve the resulting quadratic and reject the unrealistic root.

Answer 1

The Correct Option is B

This problem is a classic “overlap subtraction” setup, so it helps to picture the two crossroads as two long rectangles that share a small square patch in the middle.

1. One road, running along the length, has area $60x$; the other, running along the width, has area $40x$; but the small central square of area $x^2$ where they cross has been counted in both, so it must be subtracted once.
2. Total road area $= 60x + 40x - x^2 = 100x - x^2$, and this equals $291$.
3. Rearranging: $x^2 - 100x + 291 = 0$.
4. The quadratic factors neatly as $(x-3)(x-97)=0$, giving roots $3$ and $97$.
5. Since the road cannot be wider than the park itself (40 m), only $x=3$ makes physical sense.

So the correct answer is option B, 3 m.