Question

find the area of a square if the length of its side is doubled also find the ratio of New Year to its previous area ​

Answer 1

$\huge\mathcal\pink{ANSWER:-}$

let side of first square = s

area of square = s x s = s²

now , sides doubled

2s x 2s = 4s²

now ratio

s² : 4s²

1:4

Answer 2

Correct Question:-

Find the area of a square if the length of its side is doubled Also find the ratio of new area to its previous area.

To find:-

• The area of a square if the length of its side is doubled.
• Ratio of new area to its original area.

Solution:-

As we are not given with the measure of the side of the square, let us assume the side of the square to be x.

Now,

We know,

✭ Area of square = (side)² sq.units.

Hence,

Area = (x)² sq.units

⇒ Area = x²

∴ The area of the original square is x² sq.units.

As per said in the question,

Let us double the side of the square.

Original side = x

Doubled side = 2 × x = 2x

Now,

Area of the new square = (2x)²

⇒ Area = 2x × 2x = 4x²

∴ The area of the new square is 4x² sq.units.

Hence,

The area of the square if the side of that square is doubled will be 4x² sq.units.

Now,

Let us find the ratio of the new area to its original area.

Ratio:-

New Area : Original Area

= 4x² : x²

⇒ 4 : 1

∴ The ratio of the new area of the square to it's original area is 4 : 1.

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