Question

If the ratio of the areas of two squares is 1:4, the ratio of their perimeters is

Answer 1

Let the side of 1st square be a
& 2nd be b

the ratio comes to be
1:2

Answer 2

The perimeter ratio of the given square is $\bold{\frac{1}{2}}$.

Solution:

Let,  

Side of a square = a

And Side of another square = b

We know that, area of a square = $(\text {side})^{2}$

Therefore, area of one square = $a^{2}$  ……….. (1)

And area of another square =  $b^{2}$……….. (2)

Given that,  

Ratio of area of two squares = $\frac{1}{4}$ ………….. (3)

From the equations 1, 2 and 3  

We get,

$\frac{a^{2}}{b^{2}}=\frac{1}{4}$

$\frac{a}{b}=\frac{1}{2}$ ……….. (4)

Now,

We know that Perimeter of a square = 4× Side

Therefore,

Perimeter of one square = 4× a

Perimeter of another square = 4× b

Hence,

Ratio of perimeter of two squares =$\frac{4 a}{4 b}=\frac{a}{b}$ ………… (5)

From the equations 4 and 5,

Ratio of perimeter of two square = $\frac{1}{2}$.