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Aptitude - Area - Discussion

Discussion Forum : Area - General Questions (Q.No. 5)
Area
5.
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?
2.91 m
3 m
5.82 m
None of these
Answer: Option
Explanation:

Area of the park = (60 x 40) m2 = 2400 m2.

Area of the lawn = 2109 m2.

Area of the crossroads = (2400 - 2109) m2 = 291 m2.

Let the width of the road be x metres. Then,

60x + 40x - x2 = 291

x2 - 100x + 291 = 0

(x - 97)(x - 3) = 0

x = 3.

Video Explanation: https://youtu.be/R3CtrAKGxkc

Discussion:
75 comments Page 7 of 8.
Theodore said:   8 years ago
What will be the LENGTH of the road? Can Anyone help me to find out the answer?
Pooja said:   7 years ago
Thank you @Ayoosh.
Shivangi goel said:   7 years ago
How this quadratic equation is formed in x?
Vijay said:   7 years ago
@Ankanna.

Your explanation really helped me. Thanks.
Himanshu said:   7 years ago
Why only square of width is taken and not length?
(1)
Sreekanth said:   7 years ago
@All.

Take:
(60-x) * (40-x).
We gets the remaining area,
Already in the questions, it gives that remaining area is 2109 m2,

Verify the equation with 3.
The equation will be satisfied.
(1)
Harika said:   7 years ago
The intersection part area should be subtracted it's area = x^2.
Area of one road along length = 40x.
Area of one road along breadth = 60x.
But the area of roads is 2400-2109 = 291.
So 40x+60x-x^2 = 291.
Solve, we get x=3.
(9)
Sly said:   7 years ago
Thanks all for explaining the answer in detail.
(1)
Sk Rahad Mannan said:   7 years ago
Thanks @Ayoosh, @Tanya.
(2)
Sekhar said:   7 years ago
60x+40x-291 = x*x.

Then what about 291?

Can you explain?
(2)
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