Question

If the sides of a square are doubled, what is the ratio of the area of the original square to that of the new square?

Answer 1

Hint: - A square is a 2-dimensional figure with 4 sides in which the length of all 4 sides are equal. The opposite sides of the square are parallel. The area of a square is ${(side)^2}$.

Complete step-by-step answer:
Let the side of the square be a unit

Hence the area of the square will be ${(side)^2}$ i.e. $a \times a = {a^2}$
Now we have to double the side of the square which means we have to multiply the side of the square by 2
Hence length of the side of new square =2 a

The area of the new square will be ${(side)^2}$ i.e. $2a \times 2a = 4{a^2}$
We have to find out the ratio of the area of the original square to that of the new square.
$\Rightarrow$ Area of Original square: Area of New Square
$\Rightarrow {a^2}:4{a^2}$
$\Rightarrow 1:4$
Therefore, the ratio of areas of the original square to that of the new square is $1:4$.

Note: - The measure of the surface enclosed by a closed figure is called its area. There are different geometrical closed shapes that exist namely square, rectangle, triangle, circle, etc. A square is a four-sided rectangular closed figure on a plane. All the sides of a square are of equal length.