Question

Kanika had a piece of cloth 1 m long and 60 cm broad. She cut it into square shaped handkerchiefs, each side measuring 20 cm, and put a lace on the boundary. How much lace is needed for the handkerchiefs?

Answer 1

Given that, the cloth is $1m$ long and $60cm$ broad.

Also, the length of the square-shaped handkerchief is $20cm$

The total area of the cloth is the combined area of all the handkerchiefs.

$\therefore$ Number of handkerchiefs $=\frac{\text{Total area of cloth}}{\text{Area of 1 handkerchief}}$

Using area of rectangle $=l\times b$ and area of square $=a^2$, we get:

Number of handkerchiefs $=\frac{100\times 60}{20\times 20}=15$ $[1m=100cm]$

Length of lace required for $1$ handkerchief $=$ perimeter of $1$ handkerchief

Hence, total lace required for $15$ handkerchiefs $=$ perimeter of $15$ handkerchief

$\Rightarrow 15\times (4\times 20)$ [Perimeter of square $=4a$]

$=15\times 80$

$=1200cm$

Hence, $1200cm$ lace will be needed for all handkerchiefs.