Question

How many tiles, square in shape of side 16 cm, will be required to pave a rectangle of dimensions
 6.4m $ \times $ 5m?

Answer 1

Hint: First of all, we need to convert the length of the square from centimeter to meter and then we will be finding the perimeters of both the square and rectangle. Now, as we are paving a rectangle with square tiles, the perimeter of n number of tiles must be equal to the perimeter of the rectangle and we have the perimeter of 1 tile. So, using cross multiplication, we will get our answer.

Complete step-by-step answer:
In this question, we are given that we have to use square tiles to pave the rectangle and we are given the dimensions of the square and rectangle both.
Given data: Length of square $ = 16 $ cm
Length of rectangle $ = 6.4 $ m
Breadth of rectangle $ = 5 $ m
Now, let us find the perimeter of the square and rectangle both.
So, the perimeter of the square is given by adding all its length 4 times.
First of all, the measurements of the rectangle are given in meters and that of squares in centimeters. O, let us convert the length of the square from centimeter to meter.
 $
  1m = 100cm \\
  ?m = 16cm \;
  $
Cross multiply and we will get
 $ \Rightarrow $ Length of square in m $ = \dfrac{{16 \times 1}}{{100}} = 0.16m $
Now, let us find the perimeter.
 $ \Rightarrow $ Perimeter of square $ = 4l = 4 \times 0.16 = 0.64m $
Hence, the perimeter of one tile is 0.64m.
Now, let us find the perimeter of the rectangle.
 $ \Rightarrow $ Perimeter of rectangle $ = 2\left( {l + b} \right) $
 $
   = 2\left( {6.4 + 5} \right) \\
   = 2\left( {11.4} \right) \\
   = 22.8m \;
  $
Hence, the perimeter of the rectangle is 22.8m.
Now, we are paving square tiles on a rectangle, so the perimeter of those n number of tiles must be equal to the perimeter of the rectangle.
 $ 1 $ tile $ = 0.64m $
 $ n $ tiles $ = 22.8m $
Cross multiply, we get
 $ \Rightarrow $ Number of tiles $ = \dfrac{{22.8 \times 1}}{{0.64}} = 35.625 $
Therefore, we will be requiring approximately 36 square tiles for paving a rectangle of dimensions 6.4m $ \times $ 5m.

Note: Here note that the most important part of the question is the units of the given measurements. The units of the given measurements must always be the same. Either in centimeters or either in meters only. So, while solving these types of questions, check for the given units first and convert them if not the same.