if the side of a square is increased by 150 percent.by what percent does the area increase?
If you mean that the side is 150% as big, then
1.5^2 = 2.25
so, the area increased by a factor of 225%
But, if you really mean it increased by 150%, that is, it is now 2.5 times as big, then the area is now 6.25 times as big, so it increased by 525%
To find the percentage increase in the area of a square when its side is increased by 150 percent, follow these steps:
1. Start with the original side length of the square. Let's assume it is 'x' units.
2. Calculate the original area of the square using the formula: Area = Side^2
Original Area = x^2
3. Increase the side length by 150 percent. To do this, multiply the original side length by 1 + (150/100).
New side length = x * (1 + 150/100)
4. Calculate the new area of the square using the formula: Area = Side^2
New Area = (x * (1 + 150/100))^2
5. Find the percentage increase in the area by subtracting the original area from the new area, dividing by the original area, and multiplying by 100.
Percentage Increase = ((New Area - Original Area) / Original Area) * 100
By following these steps, you can determine the percentage increase in the area of the square when its side is increased by 150 percent.
To calculate the increase in the area of a square when its side is increased by 150 percent, we need to follow a step-by-step process:
Step 1: Understand the problem and gather information.
The problem states that the side of the square is increased by 150 percent. We need to find the percent increase in its area.
Step 2: Determine the initial side length of the square.
Let's assume the initial side length of the square is "x". This will be our reference point for calculations.
Step 3: Calculate the new side length of the square.
Since the side length is increased by 150 percent, we need to add 150 percent of "x" to "x". Mathematically, the new side length can be calculated as:
New side length = x + (150/100) * x = x + (1.5 * x)
Step 4: Calculate the new area of the square.
The area of the square is given by the formula: Area = Side length * Side length. Using the new side length calculated in Step 3, the new area can be calculated as:
New area = (x + (1.5*x)) * (x + (1.5*x))
Step 5: Calculate the increase in area.
The increase in area can be found by subtracting the initial area from the new area and then dividing it by the initial area. Mathematically, it can be calculated as:
Increase in area = [(New area - Initial area) / Initial area] * 100
In this case, the initial area is x * x and the new area is (x + (1.5*x)) * (x + (1.5*x)). Substituting these values in the formula, we get:
Increase in area = [(x + (1.5*x)) * (x + (1.5*x)) - x * x) / (x * x)] * 100
Simplifying the equation, we get:
Increase in area = [2.25 * x^2 - x^2] / x^2 * 100
Increase in area = (1.25 * x^2) / x^2 * 100
Increase in area = 1.25 * 100 = 125%
Therefore, when the side of a square is increased by 150 percent, the area increases by 125 percent.