Question

A rectangular plot of land measures 105 m by 84 m .A path of uniform width 2.5 m is to be constructed all around inside the plot. Find
A) Area of path inside the plot
B) Cost of constructing the path at the rate of RS. 7.50 per m square

Answer 1

Hint: Area of path will be area of external rectangle – area of inner rectangle .
Firstly we find the internal dimension by subtracting width two times from outer length to get inner length and for internal breadth we will subtract width two times from outer breadth. Then we will find the internal area .After this we will find the area of the path and then we will calculate the cost of constructing the path.

Formula used: $area\,of\,rec\tan gle\,\, = \,length \times \,breadth$

Complete step-by-step answer:
We have
length of outer rectangle = \[105m\]
Breadth of outer rectangle =\[\;84m\]
Now we have to find area of inner rectangle
So length of inner rectangle will be \[ = 105m-2\left( {2.5} \right)m = \left( {105-5} \right)m = 100{{ }}m\]
Similarly breadth of inner rectangle will be \[ = 84m - 2\left( {2.5} \right)m = \left( {84 - 5} \right)m = 79{{ }}m\]
Now we will find area of outer rectangle and inner rectangle
We know that,
$area\,of\,rec\tan gle\,\, = \,length \times \,breadth$
Area of outer rectangle \[ = 105m \times 84m = 8820{m^2}\]
Area of inner rectangle \[ = 100m \times 79m = 7900{m^2}\]
Therefore , area of path \[ = \left( {8820-7900} \right){m^2} = 920{m^2}\]
Now we will find ,
Cost of constructing the path will be = area × rate = \[920{m^2} \times 7.50{{ }}rs. = 6900{{ }}rs.\]
Hence the cost of constructing the path is 6900 Rupees.

Note: When width is inside the figure then for new dimensions​ of the rectangle we subtract width twice from length and breadth . When width is outside the figure then for new dimensions of rectangle we add width twice to length and breadth .