Question

How many tiles, each of the area 400 ${cm}^{2}$ will be needed to pave a footpath which is 2 m wide and surrounds a grass plot 25 m long and 13 m wide?

Answer 1

Hint – In this question use the property that the area of the rectangle is length into breadth and when a footpath is surround the rectangular grass plot the length of the footpath is increased from both side same for the breadth of the footpath so use these concepts to reach the solution of the question.

Complete step-by-step answer:

Area of the tiles = 400 ${cm}^{2}$.
Length and the breadth of the rectangular grass plot is 25 m and 13 m as shown in the figure.
Now as we know 1m = 100 cm.
So length of the rectangular grass plot = L = 25(100) = 2500 cm.
And the width or breadth of rectangular grass plot = B = 13(100) =1300 cm.
Now as we know that the area of the rectangle is the product of length and width of the rectangle.
So the area of the rectangular grass plot, A = 2500(1300) = 3250000 cm2.
Now a footpath 2 m wide surrounds the rectangular grass plot as shown in the figure.
So the new length of the plot including the width of the footpath = L’ = 25 + 2 + 2 = 29 m = 2900 cm.
And the new breadth of the plot including the width of the footpath = B’ = 13 + 2 + 2 = 17 m = 1700 cm.
So the new area of the rectangular grass plot including the footpath, A’ = L’B’ = 2900(1700) = 4930000 cm2.
So the area of the footpath is the difference of the area of the rectangular grass plot including the footpath and the area of the rectangular grass plot.
So the area of the footpath (${A_f}$) = 4930000 – 3250000 = 1680000 cm2.
Now we have to pave the footpath by the tiles whose area is = 400 cm2.
So the number of tiles used to pave the footpath is the ratio of the area of the footpath to the area of the one tile.
So the number of tiles used to pave the = $\dfrac{{1680000}}{{400}} = 4200$
So 4200 tiles are used to pave the footpath.
Hence option (A) is the correct answer.

Note – Whenever we face such types of questions first of all draw the pictorial representation of the problem as above then using the area formula of the rectangle which is stated above calculate the area of the footpath as above then the number of tiles used to pave the footpath is the ratio of the area of the footpath to the area of the one tile so just simply this as above, we will get the required answer.