Question

How many square tiles of side 40 cm will be required to pave a footpath which is 2 m wide and surrounds a rectangular plot 80m by 44m?

Answer 1

Hint: In this question, we will use the area of rectangle and square formula i.e., $l \times b$, where $ = 3200$ is the length and $b$ is the breadth of the rectangle is the area of rectangle and ${a^2}$ is the area of square where $a$ is the side of the square, and first we will find the area of footpath by subtracting the area of outer fence from area of the rectangular plot, and finally we divide the area of footpath by the area of square to find the number of tiles.

Complete step-by-step answer:
Given dimensions of the rectangular plot are 80m and 40m, i.e, length will be 80m and breadth will be 40m, and the footpath is 2m wide.
Now we have to find a number of square tiles of length 40cm that will be required by the footpath.
Now we will find the area of the rectangular path by using area of rectangle i.e., $l \times b$, where ${a^2}$ is the length and $b$ is the breadth of the rectangle,
So, here $l = 80m,b = 44m$,
Now by substituting the values we get,
$\Rightarrow$Area of rectangular plot$ = 80 \times 44$,
$\Rightarrow$Area of rectangular plot$ = 3520{m^2}$,
Now width of the footpath = 2m,
Now length of the outer rectangle will be $80 + 2 + 2 = 84{m^2}$, and breadth of the outer rectangle will be $44 + 2 + 2 = 48{m^2}$,
Now area of outer rectangle = $ = 84 \times 48$,
$\Rightarrow$Area of outer rectangular plot$ = 4032{m^2}$,
Now area of footpath = Area of outer rectangular plot$ - $area of inner rectangular plot i.e.,
$\Rightarrow$Area of footpath = $4032 - 3250$ ,
$\Rightarrow$Area of footpath$ = 512{m^2}$,
Now we will find the area of square by using area of square formula i.e., ${a^2}$, where $a$ is the side of the square,
Now here side of the square= a = 40cm,
$\Rightarrow$Area of square =${\left( {40} \right)^2}$,
$\Rightarrow$Area of square$ = 1600c{m^2}$,
Now converting $c{m^2}$to ${m^2}$,we know that $1m = \dfrac{1}{{100}}cm$,we get ,
$\Rightarrow$Area of square$ = 1600{\left( {\dfrac{1}{{100}}} \right)^2}{m^2}$
$\Rightarrow$Area of square$ = 1600\left( {\dfrac{1}{{10000}}} \right){m^2}$,
$\Rightarrow$Area of square$ = \dfrac{{16}}{{100}}{m^2}$,
$\Rightarrow$Area of square$ = \dfrac{4}{{25}}{m^2}$,
Now we have find the number of tiles required to pave a footpath which is 2 m wide, i.e.,
$\Rightarrow$ Number of titles$ = \dfrac{{{\text{Area of footpath}}}}{{{\text{Area of single square tile}}}}$,
Now we have the values so substituting the values we get,
$\Rightarrow$Number of titles$ = \dfrac{{{\text{512}}}}{{\dfrac{4}{{25}}}}$
$\Rightarrow$Number of tiles$ = \dfrac{{{\text{512}} \times 25}}{4}$,
$\Rightarrow$Number of tiles$ = 3200$.

$\therefore $ The number of square tiles of side 40 cm required to pave a footpath which is 2 m wide and surrounds a rectangular plot 80m by 44m are 3200.

Note:
 We can also solve the question by finding the number of tiles that can paved in total and the number of tiles can be paved in the rectangular plot,
$\Rightarrow$Total number of titles $ = \dfrac{{{\text{Area of footpath}}}}{{{\text{Area of single square tile}}}}$,
$\Rightarrow$Total number of tiles $ = \dfrac{{4032}}{{\dfrac{4}{{25}}}}$
$\Rightarrow$Total number of tiles $ = 25200$,
$\Rightarrow$Number of tiles can be paved in plot $ = \dfrac{{{\text{plot area}}}}{{{\text{Area of a single square}}}}$,
$\Rightarrow$Number of tiles can be paved in plot $ = \dfrac{{3520}}{{\dfrac{4}{{25}}}}$,
$\Rightarrow$Number of tiles can be paved in plot $ = 22000$,
$\Rightarrow$Now number of tiles = total number of tiles $ - $ number of tiles paved in plot
$\Rightarrow$Required number of tiles $ = 25200 - 22000$
$\Rightarrow$Required number of tiles $ = 3200$.