the length of a square increases by 20%. By what percentage does the area of the square increase?
Let's assume the length of the square is L.
If the length increases by 20%, then the new length is 1.2L.
The area of a square is given by A = L^2.
Therefore, the new area is (1.2L)^2 = 1.44L^2.
The increase in the area is given by (1.44L^2 - L^2)/L^2 = 0.44.
To express this increase as a percentage, we multiply by 100% to get 0.44 * 100% = 44%.
Therefore, the area of the square increases by 44%.
To find the percentage increase in the area of a square when its length increases by 20%, you can follow these steps:
Step 1: Let's assume the original length of the square is "L"
Step 2: The original area of the square is given by the formula A = L^2
Step 3: The new length of the square is "L" + 20% of "L", which can be written as L + 0.2L = 1.2L (After simplification)
Step 4: The new area of the square is given by the formula A' = (1.2L)^2
Step 5: Simplifying the equation above, we get A' = 1.44L^2
Step 6: To find the percentage increase, we need to compare the difference between the new area (A') and the original area (A) divided by the original area (A).
Step 7: The percentage increase can be calculated using the formula (A' - A) / A * 100%.
Let's calculate the percentage increase in the area: