Question

If the length of the side of a square is doubled, what is the ratio of the areas of the original square to the area of the new square?

Answer 1

Answer:

The ratio of the areas of the original square to the area of the new square is 1 : 4.

Step-by-step explanation:

Given :

Length of the side is = doubled

To find :

The ratio of areas of original square to area of the new square

Solution :

Let the side of the original square be y

⭐ Area of the Square = Side× Side

⇒ y × y

⇒ y²

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As the side of the square is doubled, multiply the side by 2.

⇒ y × 2

⇒ 2y ..............[New Side]

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⭐ Area of the Square = Side × Side

⇒ 2y × 2y

⇒ 4y²

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⭐ Ratio of the area of original square to the area of new square -

⇒ y² : 4y²

⇒ $\sf{\dfrac{y^{2}}{4y^{2}}}$

⇒ 1 : 4

∴ The ratio of the areas of the original square to the area of the new square is 1 : 4.

Answer 2

Answer:

The Ratio is 1 : 4.

Step-by-step explanation:

Consider the side of the first Square as 'a'.

The formula to find out the area of a square is = Side²

$\longrightarrow$ a × a = a²

According to the question, the side need to be doubled, new side =

$\longrightarrow$ a × 2 = 2a

Area of the new square -

$\longrightarrow$ 2a × 2a

$\longrightarrow$ 4a²

Ratio of the old square to the new square's area is -

$\longrightarrow$ a² : 4a²

$\longrightarrow$ 1 : 4

.°. The Ratio is 1 : 4.