Question

48.
If the ratio of the area of two squares is 9:1, the
ratio of the their perimeters is
1) 9:1 20 3:1 3) 3:4 4) 1:3

Answer 1

Answer ::

The ratio of their perimeters are 3:1.

[ Option. b. ] is the correct option.

Step-by-step explanation ::

To Find :-

• The ratio of the perimeter of two squares

Solution :-

Given that,

• The ratio of the area of two squares = 9:1

As we know that,

Area of square = a²

Where,

• a = side of square

Let us assume a side of square as $\sf{{a}_{1}}$ and the other side of square as $\sf{{a}_{2}}$

First we need to find out the side of a square,

The sides of the two squares are :-

$\underline{\bf{given \: that}} \\ \sf{\dfrac{Area \: of \: square}{Area \: of \: square} = \dfrac{9}{1}} \\ \\ \\ \therefore \: \sf{ \mapsto \: \dfrac{{a_1}^{2}}{{a_2}^{2}} = \dfrac{9}{1}} \\ \\ \\ \sf{ \mapsto \: \dfrac{{a}_{1}}{{a}_{2}} = \sqrt{\dfrac{9}{1}}} \\ \\ \\ \sf{ \mapsto \: \dfrac{{a}_{1}}{{a}_{2}} = \dfrac{3}{1}}$

The ratio of squares are 3:1.

According the question,

The perimeter of square is,

As we know that,

Perimeter of square = 4 × a

Where,

• a = side of square

$\sf{\dfrac{Perimeter \: of \: square}{Perimeter \: of \: square} = \dfrac{4 \times a_1}{4 \times a_2}} \\ \\ \\ \sf{ \mapsto \: \dfrac{{Perimeter}_{({a}_{1})}}{{Perimeter}_{({a}_{2})}} = \dfrac{4}{4} \times \dfrac{3}{1}} \\ \\ \\ \sf{ \mapsto \: \dfrac{{Perimeter}_{({a}_{1})}}{{Perimeter}_{({a}_{2})}} = \cancel{ \dfrac{4}{4}} \times \dfrac{3}{1}}$

The ratio of their perimeter of squares are 3:1.