A square park has a 3metre wide road inside it running along its side the area occupied by the road is 1764 square metres .what ia the perimeter along the outer edge.
Answers
A park, square in shape has a 3 metre wide road inside it running along its sides.
Let the sides of the square shaped park be x metres
Thus outer area of park = (sides)^2 = x^2
Inner length of park excluding 3 m wide road
= x - (3 + 3)
= x - 6
Inner area of Park excluding road = (sides)^2 = (x - 6)^2
Area of road = Outer area of sqare park - inner area of square park excluding road
As per statement the area occupied by the road is 1764 square meter. Accordingly
1764 = x^2 - (x - 6)^2
x^2 - x^2 - 36 + 12x = 1764
—36 + 12x = 1764
12x = 1764 + 36
12x = 1800
x = 1800/12
x = 150 metres
Outer edge = 150 metres
Perimeter of outer edge of road
= 2 (side + side)
= 2 (2 sides)
= 4 × sides
= 4 × 150 metres
= 600 metres
Thus the perimeter of the outer edge of the road is 600 m.
Answer: the perimeter along the outer edge of the road is 600 metres.
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