If each side of a square is increased by 50%, the area of the square is increased by
A)50%
B)100%
C)125%
D)225%
help please!!!!!!!!!!
To find the answer, we need to understand the relationship between the side length of a square and its area.
The area of a square is calculated by squaring its side length. In other words, if the side length is "s," the area is given by s^2.
Let's consider a square with a side length of "s." If each side of the square is increased by 50%, the new side length would be 1.5 times the original side length, or 1.5s.
The new area of the square can be calculated by squaring the new side length, giving us (1.5s)^2.
Expanding (1.5s)^2 = 2.25s^2.
To find the percentage increase in area, we need to calculate the difference between the new area (2.25s^2) and the original area (s^2), and then express that difference as a percentage of the original area.
The difference between the new and original areas is 2.25s^2 - s^2 = 1.25s^2.
To express the difference as a percentage of the original area, we divide the difference by the original area (s^2) and multiply it by 100:
(1.25s^2 / s^2) * 100 = 125%
Therefore, the area of the square is increased by 125%, which corresponds to option C) 125%.