Question

If the ratio between the perimeter of two squares is 1 : 2 then the ratio between their areas is

Answer 1

Answer:

1:4 hope it helps you

Step-by-step explanation:

Perimeter is in the ratio = 1:2

Let side of one square is x and other square is y

So,

ATQ

the perimeter of square 1 / perimeter of the square 2 = 1/2

$\frac{4x}{4y} = \frac{1}{2} \\\\\frac{x}{y} = \frac{1}{2}$

Squaring both sides

x^2/y^2 = 1^2/2^2

$\frac{x^2}{y^2} = \frac{1}{4}$

So, the ratio is 1:4

Answer 2

Answer:

The ratio between the areas of two squares is 1 : 4.

Step-by-step explanation:

Given, that the ratio between the perimeter of two squares is 1 : 2

We know that,

The perimeter of a square = 4a (where a is the side of a square)

Area of a square = $a^{2}$  (where a is the side of a square)

According to the question,

$\frac{Perimeter of square (s1)}{Perimeter of square (s2)} = \frac{4a1}{4a2} = \frac{1}{2}$

⇒ $\frac{a1}{a2} = \frac{1}{2}$

Therefore the areas of two squares can be equated as,

$\frac{Area of square(s1)}{Area of square(2)} = \frac{a1^{2} }{a2^{2} }$

∴ $\frac{a1^{2} }{a2^{2} } = \frac{1^{2} }{2^{2} }$ $= \frac{1}{4}$

So, the ratio of areas of two squares is 1 : 4