Question

If the sides of the two squares are in the ratio 3:1 then the ratio of their areas is: *
1 point
1:3
9:1
1:9
27:1​

Answer 1

Answer :-

• The ratio of their areas are 9:1.

[ Option. b. ] 9:1 is the correct option.

Step-by-step explanation :-

To Find :-

• The ratio of their areas [ two given squares ]

Solition :-

Given that,

• The sides of two squares are in the ratio of 3:1

According the question,

• The ratio of their areas,

As we know that,

Area of square = ( side )² sq. units, Hence, the area of their areas are :-

$\sf{\longmapsto \: {Area \: of \: two \: squares}_{(ratio)} = \bigg( \dfrac{side}{side}\bigg)^{2}} \\ \\ \\ \sf{\longmapsto \: \bigg( \dfrac{3}{1}\bigg)^{2}} \\ \\ \\ \sf{\longmapsto \: \dfrac{3}{1} \: \times \: \dfrac{3}{1}} \\ \\ \\ \sf{\longmapsto \: \dfrac{3 \times 3}{1 \times 1}} \\ \\ \\ \sf{\longmapsto \: \dfrac{9}{1}} \\ \\ \\ \sf{\longmapsto \: \purple{\underline{\boxed{9:1}}}} \\ \\ \underline{\sf{\therefore \: Ratio \: of \: areas = 9:1}}$

Hence,

• The ratio of their areas are 9:1.