Question

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

• A. 2.91 m
• B. 3 m
• C. 5.82 m
• D. 6 m
• E. 9 m

Answer 1

The correct option is B

3 m

Area of the park = (60 $\times$ 40) m${}^2$ = 2400 m${}^2$. Area of the lawn = 2109 m${}^2$ $\therefore$Area of the crossroads = (2400 -- 2109) m${}^2$ = 291 m${}^2$ Let the width of the road be `x' metres. Then, 60x + 40x -- x${}^2$ = 291 $\iff$ x${}^2$ -- 100x + 291 = 0 $\iff$ (x -- 97) (x -- 3) = 0 $\iff$ x = 3 [$x\ne 97]$