Question

Draw two squares of different sides. Can you say they are similar? Explain. Find the ratio of their perimeters and areas. What do you observe?

Answer 1

Let us draw two squares of sides $2cm$ and $4cm$. As all the sides are in proportion $\frac{AB}{PQ}=\frac{BC}{QR}=\frac{CD}{RS}=\frac{DA}{SP}=\frac{2}{4}$
$=\frac{1}{2}$
And all the pairs of corresponding angles are ${90}^{\circ }$
So square $ABCD\sim squarePQRS$
Perimeter of $\square ABCD=4\times 2=8cm$
Perimeter of $\square PQRS=4\times 4=16cm$
Ratio of their perimeters $=8:16=1:2$ Ratio of their perimeters is same as ratio of their corresponding sides.
Area of $ABCD=2\times 2=4c{m}^2$
Area of $PQRS=4\times 4=16c{m}^2$
Ratio of their area $=4:16=1:4=1^2:2^2$
$=$ Ratio of squares of the corresponding sides.