The village playground is shaped as a square of side 40 metres. A path of width Class 9
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The village playground is shaped as a square of side 40 metres. A path of width Class 9
Question 1.
The village playground is shaped as a square of side 40 metres. A path of width s metres is created around the playground for people to walk. Find an expression for the area of the path in terms of s. Class 9
Solution:
Given:
Side of square playground = 40 metres,
Width of path = s metres
Side of the outer square
= 40 + s + s = (40 + 2s) m
∴ Area of outer square = (40 + 2s)²
= (40)² + 2(40) (2s) + (2s)²
...[∵ (a + b)² = a² + 2ab + b²]
= 1600 + 160s + 4s² m²
Area of inner square
= (40)² = 1600 m²
Area of path
= Area of outer square - Area of inner square
= (1600 + 160s + 4s²) - 1600
= (4s² + 160s) m²
= 4s (s + 40) m²
∴ The expression for the area of the path in j terms of s is 4s (s + 40) m².