2: 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?
Answers
Answer:
Let us draw two squares of sides 2 cm and 4 cm. As all the sides are in proportion
PQ
AB
=
QR
BC
=
RS
CD
=
SP
DA
=
4
2
=
2
1
And all the pairs of corresponding angles are 90
∘
So square ABCD∼square PQRS
Perimeter of □ABCD=4×2=8 cm
Perimeter of □PQRS=4×4=16 cm
Ratio of their perimeters =8:16=1:2 Ratio of their perimeters is same as ratio of their corresponding sides.
Area of ABCD=2×2=4 cm
2
Area of PQRS=4×4=16 cm
2
Ratio of their area =4:16=1:4=1
2
:2
2
= Ratio of squares of the corresponding sides.
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
Let one square(s1) be of side 4cm
and another one(s2) be of 8cm
Therefore, Perimeter(s1): 4a=4*4=16
Area(s1): a*a=4*4=16
Ratio(s1)=16:16=1:1
And, Perimeter(s2): 4a=4*8=32
Area(s2): a*a=8*8=64
Ratio(s2)=32:64=1:2
You can see in both cases we have different ratios, so we can say that both the squares are not similar.