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}  20^{2}
But the area of the path is given to be 276 square metres.
Therefore, (20 + 2x)^{2}  20^{2} = 276
(20 + 2x)^{2} = 20^{2} + 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 centimetres 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 centimetres, then find the width of the path. Use different colors to represent the path and the square plot.
