A path of 2 metres wide runs around and inside a rectangular plot of measurements 30 metres and 20 metres. Find the cost levelling the path at the rate of $2 per square metre.
the length = 30 metres, width = 20 metres, width of the path = 2 metres
Since the path runs inside this, the measurements of the inner rectangle are,
(l - 2w) and (b - 2w)
i.e (30 - 2*2) and (20 - 2*2)
i.e (30 - 4) and (20 - 4)
i.e 26 and 16
The area of the given rectangle = l * b = 30 * 20 = 60 square metres.
The area of the inner rectangle = (l - 2w)(b - 2w) = 26 * 16 = 416 square metres.
So the area of the path = lb - (l - 2w)(b - 2w)
= 600 - 416
= 184 square metres.
The cost of levelling the path at the rate of $2 per square metres.
= $ 2 * 184 = $ 368.
Directions: Read the above example carefully and answer the following questions:
- Draw a rectangular plot of side 11 centi-metres and 13 centimetres. Draw a path of width 3 centi-metres, around and outside the rectangular plot. Find the cost of leveling the path at the rate of $3 per square metre. Use different colors to represent the path and the rectangular plot.