020. A square park has a 3 metre wide road inside it running along its sides. The area occupied by the
road is 1764 sq. m. What is the perimeter along the outer edge of the road?
Answers
Given data :
- A square park has a 3 m wide road inside it running along its sides.
- The area occupied by the road is 1764 m².
To find : The perimeter along the outer edge of the road ?
Solution : Let, side of square park (with side road joined ) be x
→ Area of square park = ( side )²
→ Area of square park = x² ....( 1 )
Now, according to given, road inside square park. Hence,
Inner side of square excluding 3 m wide road.
→ Inner side of square = x - ( 3 + 3 )
→ Inner side of square = x - 6
→ Area of inner square = ( side )²
→ Area of inner square = (x - 6 )² ....( 2 )
Now, from ( 1 ) and ( 2 ) and given
→ Area pf road = [Area of square park] - [Area of inner square]
→ 1764 = x² - ( x - 6 )²
→ 1764 = x² - ( x² - 12x + 36 )
→ 1764 = x² - x² + 12x - 36
→ 1764 = 12x - 36
→ 1764 + 36 = 12x
→ 1800 = 12x. i.e.
→ x = 1800/12
→ x = 150 m .....( 3 )
Now, to find perimeter of road, we use formula of perimeter of square.
→ Perimeter of road = 4 * side
form ( 3 )
→ Perimeter of road = 4 * x
→ Perimeter of road = 4 * 150
→ Perimeter of road = 600 m
Answer : Hence, the perimeter along the outer edge of the road is 600 m.
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