When the length of a rectangle is increased by 20 percent and the width is increased by 10 percent, by what percent is the area increased?
1.2l * 1.1w = 1.32*lw
so, it grew by ??
A1 = L * W .
A2 = 1.1W * 1.2*L = 1.32LW.
A2/A1 = 1.32LW/LW = 1.32 = 132%.
132% - 100% = 32% Increase.
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To calculate the increase in the area of a rectangle when the length and width are increased by certain percentages, we can follow these steps:
1. Assume the original length of the rectangle is "L" and the original width is "W."
2. Calculate the percent increase for the length by multiplying it by 20% (or 0.2): Percent Increase in Length = L * 0.2.
3. Calculate the new length after the increase by adding the percent increase to the original length: New Length = L + (L * 0.2) = L + 0.2L = 1.2L.
4. Calculate the percent increase for the width by multiplying it by 10% (or 0.1): Percent Increase in Width = W * 0.1.
5. Calculate the new width after the increase by adding the percent increase to the original width: New Width = W + (W * 0.1) = W + 0.1W = 1.1W.
6. Calculate the area of the original rectangle: Original Area = L * W.
7. Calculate the area of the new rectangle: New Area = (1.2L) * (1.1W).
8. Calculate the percent increase in area by subtracting the original area from the new area, dividing by the original area, and then multiplying by 100: Percent Increase in Area = ((New Area - Original Area) / Original Area) * 100.
By following these steps, you should be able to calculate the percent increase in the area of the rectangle when the length is increased by 20% and the width is increased by 10%.
Let width = 2 Ft.
Length = 4 Ft..
Area = 2 * 4 = 8 Ft^2.
Width = 1.1 * 2 = 2.2 Ft.
Length = 1.2 * 4 = 4.8 Ft.
Area = L * W = 4.8 * 2.2 = 10.56 Ft.^2.
10.56/8 = 1.32 = 132%.
Increase = 132%-100% = 32%.