Question 37 of 43intermediate🔧 ApplyShort Answer3 marks

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.

Correct Answer

160s + 4s24s^{2} square metres

Exercise: END-OF-CHAPTER EXERCISES | Q: 7 | (Page 23)
For More Understanding

Explanation

The area of the path is found by subtracting the area of the inner square playground from the area of the outer square (playground + path). The inner square has an area of 40240^{2}. The outer square has a side length of 40 + 2s, making its area (40 + 2s)^2. Using the difference of squares identity, the path's area simplifies to 160s + 4s24s^{2}.

Solution Steps

  1. Step 1: Area of the inner square playground = 40240^{2} = 1600 sq. metres.

  2. Step 2: Side of the outer square including the path = 40 + s + s = 40 + 2s metres. Area of outer square = (40 + 2s)^2 sq. metres.

  3. Step 3: Area of the path = Area of outer square - Area of inner square = (40 + 2s)^2 - (40)^2.

  4. Step 4: Using the identity a2a^{2} - b2b^{2} = (a+b)(a-b), we get (40 + 2s + 40)(40 + 2s - 40) = (80 + 2s)(2s) = 160s + 4s24s^{2} sq. metres.

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