If length of the side of a square is doubled ,what is the ratio of the area of the original square to the area of the new square?write as common fraction, a decimal fraction and a percentage
When the length of the side of a square is doubled, the new square will have sides that are twice as long as the original square.
The area of a square is given by the formula A = s^2, where A is the area and s is the length of a side.
Let's say the original square has side length x.
The area of the original square is A = x^2.
When the side length is doubled, the new square will have side length 2x.
The area of the new square is A' = (2x)^2 = 4x^2.
The ratio of the area of the original square to the area of the new square is:
A/A' = x^2/4x^2 = 1/4 = 0.25
This can also be expressed as a percentage: 0.25 x 100% = 25%.
So, the ratio of the area of the original square to the area of the new square is 1/4, 0.25, or 25%.