Question

A colored cloth \[1.75{\text{ }}meter\] long and \[105cm\] wide is made into a handkerchiefs of side \[35{\text{ }}cm\]. The number of handkerchiefs on the side \[35cm\].
A. \[10\]
B. \[15\]
C. \[25\]
D. \[35\]​

Answer 1

Hint: We have been given a color cloth of \[1.75m\] long and \[105cm\] wide. Square handkerchiefs have to be made up of side \[35cm\] from the color cloths. So firstly we have to convert the length of cloth from meters to centimeters. Now both the length and breadth of colored cloth are in the same unit. So, we can find the area of colored cloth. We have given the side of the square handkerchief. We calculate the area of one handkerchief. After that we divide the area of the colored cloth by the area of the handkerchief. After that we divide the area of the colored cloth by the area of the handkerchief and the result will be the number of handkerchiefs that can be made from the cloth.

Complete step-by-step answer:
 We have given that the length of colored cloth is \[1.75m\]. We change meters into centimeters.
\[1meters = 100cm\]
\[1.75{\text{ }}meters = 1.75 \times 100\]cm
\[ \Rightarrow \]\[ 175cm\]
So length of the coloured cloth \[ = 175cm\]
Breadth of the coloured cloth \[ = 105cm\]
The shape of the coloured cloth will be rectangular. So area of colored cloth \[ = {\text{ }}length \times breadth\]
Area of colored cloth \[ = 175 \times 105\]
\[ \Rightarrow \]\[ 18375{\text{ }}sq{\text{ }}cm\]
Now we have given the side of the handkerchief \[ = 35cm\].
Shape of the handkerchief is square.
So area of the handkerchief \[ = {\text{ }}side \times side\]
Area of handkerchief \[ \Rightarrow 35 \times 35{\text{ }} = 1225{\text{ }}sq.{\text{ }}cm\]
Now we calculate the number of handkerchief can be made which is given as \[ = \dfrac{{\;Area{\text{ }}of{\text{ }}coloured{\text{ }}cloths}}{{Area{\text{ }}of{\text{ }}one{\text{ }}handkerchief}}\]
\[ \Rightarrow \] \[ \dfrac{{\;18375}}{{1225}}\]
\[ \Rightarrow \] \[ 15\]

So, the number of square handkerchiefs that can be made from the colored cloth is \[15\].

Note: A square is a closed, two dimensional shape with four equal sides. A square is a quadrilateral and all four interior angles are equal to \[90^\circ \]. It has 4 sides and 4 vertices. We can find the shape of a square in our surroundings or in our daily life such as a board, chess board, a wall clock and in a slice of bread.