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

1 answer

If the length of the side of the original square is doubled, the new square will have sides that are twice as long as the original square.

The area of a square is calculated by squaring the length of one side.

Let's assume that the original square has side length "x". The area of the original square is then x^2.

If the length of the side is doubled, the new square will have side length "2x". The area of the new square is then (2x)^2 = 4x^2.

The ratio of the area of the original square to the area of the new square is therefore:

Original square area : New square area
x^2 : 4x^2

Simplifying this ratio, we can divide both the numerator and denominator by x^2:

Original square area : New square area
1 : 4

Therefore, the ratio of the area of the original square to the area of the new square is 1:4.