Question

If the ratio of area of two square is 9:1. Then find the ratio of their perimeter

Answer 1

$\bigstar \bf \sf \underline{\underline{Given:-}}$

• The ratio of area of two squares is 9:1 .

$\bigstar \bf \sf \underline{\underline{To\ find:-}}$

• The ratio of their perimeter.

$\bigstar \bf \sf \underline{\underline{Solution:-}}$

We know :

-------------------------------------

❥ Area of square = S²

❥ Perimeter of square = 4S.

Where 's' is side of square.

---------------------------------------

Acc to question :-

=> Area of first square / Area of second square = 9:1

$\implies \sf \frac{S_1 ^2}{S_2^2} = \frac{9}{1} \\\\\\\implies \sf \frac{S_1}{S_2} =\sqrt{ \frac{9}{1} }\\\\\\\implies \sf \frac{S_1}{S_2} =\frac{3}{1}$

And,

$\implies \sf \frac{Perimeter\ of\ first\ square}{Perimeter\ of\ second\ square} = \frac{4S_1}{4S_2} \\\\\\\implies \sf \frac{4S_1}{4S_2}=\frac{4}{4} \times \frac{3}{1} \\\\\\\implies \boxed{\pink{\sf \frac{S_1}{S_2}=\frac{3}{1} }}$

Hence,Ratio of perimeter is 3:1.

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HOPE IT HELPS !

Answer 2

$\bigstar \bf \sf \underline{\underline{Given:-}}$

The ratio of area of two squares is 9:1 .

$\bigstar \bf \sf \underline{\underline{To\ find:-}}$

The ratio of their perimeter.

$\bigstar \bf \sf \underline{\underline{Solution:-}}$

We know :

-------------------------------------

❥ Area of square = S²

❥ Perimeter of square = 4S.

Where 's' is side of square.

---------------------------------------

Acc to question :-

=> Area of first square / Area of second square = 9:1

$\implies \sf \frac{S_1 ^2}{S_2^2} = \frac{9}{1} \\\\\\\implies \sf \frac{S_1}{S_2} =\sqrt{ \frac{9}{1} }\\\\\\\implies \sf \frac{S_1}{S_2} =\frac{3}{1}$

And,

$\implies \sf \frac{Perimeter\ of\ first\ square}{Perimeter\ of\ second\ square} = \frac{4S_1}{4S_2} \\\\\\\implies \sf \frac{4S_1}{4S_2}=\frac{4}{4} \times \frac{3}{1} \\\\\\\implies \boxed{\pink{\sf \frac{S_1}{S_2}=\frac{3}{1} }}$

Hence,Ratio of perimeter is 3:1.

___________________

HOPE IT HELPS !