Example:
A path of uniform width runs around and outside a square plot of side 20 metres. If the area of the path is 276 square metres find its width.
Solution:
Let the width of the path be x metres.
Now each side of the given square plot = 20 metres.
Therefore, each side of the outer square = (20 + 2x) metres, because the path runs outside.
The are of the path = (The area of outer square) - (The area of the inner square)
= (20 + 2x)2 - 202
But the area of the path is given to be 276 square metres.
Therefore, (20 + 2x)2 - 202 = 276
(20 + 2x)2 = 202 + 276
(20 + 2x)2 = 400 + 276
(20 + 2x)2 = 676
Take square roots on both sides
Ö(20 + 2x)2 = Ö676
20 + 2x = 26
2x = 26 - 20
2x = 6
x = 6/3
\ The width of the path = 3 metres.
Directions: Read the above example carefully and answer the following questions:
- Draw a square plot of side 12 centi-metres and label its sides. Draw a path of uniform width around and outside the square plot. If the area of the path is given by 256 square centi-metres, then find the width of the path. Use different colors to represent the path and the square plot.
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