Question

How many envelopes of size \[20cm \times 30cm\] be made from a rectangular sheet of paper measuring $5m \times 3m$?

Answer 1

Hint- In order to deal with this question first we will convert meter unit in centimetre unit further we will find the area of single envelope and rectangular sheet by using the formula of area of rectangle as product of length and width, at last by dividing the area of rectangular sheet by area of single envelope we will get the required answer.

Complete step-by-step answer:
Given that length of an envelope $ = 30cm$
Width of an envelope $ = 20cm$
Length of rectangular sheet $\because 1m = 100cm$
$ = 5m = 5 \times 100cm = 500cm$
Width of an envelope $\because 1m = 100cm$
\[ = {\text{ }}3m{\text{ }} = {\text{ }}3{\text{ }} \times 100{\text{ }} = {\text{ }}300{\text{ }}cm\]
As we know that area of rectangle is given as
Area of rectangle = length \[ \times \] width of rectangle
Now we will calculate area of envelope and area of rectangular sheet by using the above formula
Therefore, area of an envelope = length \[ \times \] width of envelope
By substituting the given dimensions of envelope we get
\[ = 20cm \times 30cm = 600c{m^2}\]
Similarly , area of rectangular sheet = length \[ \times \] width of rectangular sheet
By substituting the given dimensions of sheet we get
\[ = 500cm \times 300cm = 150000c{m^2}\]
As we know that number of envelopes made by rectangular sheet = area of rectangular sheet \[/\] area of an envelope
Substitute obtained values in above formula we get
\[
   \Rightarrow 150000/600 \\
   \Rightarrow 250 \\
\]
Hence the total number of envelopes made by a rectangular sheet is 250.

Note- A rectangle contains two parameters, first is length and second is breath. We can get the area covered by a rectangle by using formula =length\[ \times \]breath\[ = (l \times b)\]. Where \[l\] is the length of the rectangle and \[b\] is the breath of the rectangle. The perimeter of the rectangle is given by\[ = 2(l + b)\].