Question : A rectangular park, 60 metres long and 40 metres wide, has two concrete crossroads running in the middle of the park, and the rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. metres, then the width of the road is:
Option 1: 3 metres
Option 2: 5 metres
Option 3: 6 metres
Option 4: 2 metres
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Correct Answer: 3 metres
Solution :
Given:
A rectangular park, 60 meters long and 40 metres wide.
Area of the park = (60 × 40) = 2400 sq. metres
Area of the lawn = 2109 sq. metres
So, the area of the crossroads = (2400 – 2109) = 291 sq. metres
Let the width of the road be $x$ metres.
Then, $60x + 40x - x^2 = 291$
⇒ $x^2 - 100x + 291 = 0$
⇒ $(x - 97) (x -3) = 0$
$\therefore x = 3$
$x$ cannot be 97 because the width of the road cannot be larger than the length and breadth.
Hence, the correct answer is 3 metres.
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