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My society parking is 30 m long and 20 m wide has two crossroads running in the middle of the parking and rest of the parking has been used as a playground. If the area of the playground is 200 sq. m, then what is the width of the road?

My society parking is 30 m long and 20 m wide has two crossroads running in the middle of the parking and rest of the parking has been used as a playground. If the area of the playground is 200 sq. m, then what is the width of the road? Correct Answer 10 m 

Given:

Length and breadth of parking is 30m and 20 m respectively.

Formula:

Area of the rectangle = L × B (L = length and b = breadth) 

Total area of the road = (Area of road parallel to length) + (Area of road parallel to breadth) – (Area of square at the intersection of roads)

Calculations:

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

Area of rectangle - Area of road = 200

⇒ 30 × 20 − = 200

⇒ 600 − = 200

⇒ x2 − 50x = 200 – 600

⇒ x2 – 50x + 400 = 0

⇒ (x – 40)(x - 10) = 0

⇒ x = 40, 10

consider x = 10 m (x = 40 > max length of parking)

∴ The width of the road is 10 m.

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