Suppose the length and the width of the sandbox are doubled.
a. Find the percent of change in the perimeter.
The percent of change in the perimeter is a
% increase.
b. Find the percent of change in the area.
The percent of change in the area is a
% increase.
a. 100% increase
b. 300% increase
boom.
a. P1 = 2L + 2W. = 2(L+W).
P2 = 4L + 4W.= 4(L+W).
P2/P1 = 4(L+W)/2(L+W) = 2.0 = 200%.
200% - 100% = 100% Increase.
b. A1 = L * W.
A2 = 2L * 2W = 4(L*W).
A2/A1 = 4(L*W)/(L*W) = 4.0 = 400%.
400% - 100% = 300% Increase.
To find the percent of change in the perimeter, we need to consider that the length and the width of the sandbox have been doubled. Let's assume the original length and width of the sandbox are L and W, respectively.
a. Find the percent of change in the perimeter:
The original perimeter of the sandbox is 2L + 2W.
When the length and width are doubled, the new length becomes 2L, and the new width becomes 2W. So the new perimeter is 2(2L) + 2(2W) = 4L + 4W.
To find the percent of change, we need to calculate the difference between the new perimeter and the original perimeter, and then divide that difference by the original perimeter. Finally, multiply the result by 100 to get the percentage.
Percentage change in perimeter = ((new perimeter - original perimeter) / original perimeter) * 100
= ((4L + 4W - (2L + 2W)) / (2L + 2W)) * 100
= ((2L + 2W) / (2L + 2W)) * 100
= 100%
Therefore, the percent of change in the perimeter is a 100% increase.
b. Find the percent of change in the area:
The original area of the sandbox is L x W.
When the length and width are doubled, the new length becomes 2L, and the new width becomes 2W. So the new area is (2L) x (2W) = 4LW.
To find the percent of change in the area, we need to calculate the difference between the new area and the original area, and then divide that difference by the original area. Finally, multiply the result by 100 to get the percentage.
Percentage change in area = ((new area - original area) / original area) * 100
= ((4LW - (LW)) / (LW)) * 100
= ((3LW) / (LW)) * 100
= 300%
Therefore, the percent of change in the area is a 300% increase.