If the length of a rectangle is increased by 120%, and its width is decreased by 20%, what happens to the area of the rectangle.
old length --x
old width -- y
old area = xy
new length -- 1.2x
new width -- .8y
new area = (1.2x)(.8y) = .96xy
new area is reduced by 4%
THANKS!
To determine what happens to the area of the rectangle, we need to follow these steps:
Step 1: Let's assume the initial length of the rectangle is L and the initial width is W.
Step 2: The length of the rectangle is increased by 120%, which means it will be L + (120/100)*L = L + 1.2L = 2.2L.
Step 3: The width of the rectangle is decreased by 20%, which means it will be W - (20/100)*W = W - 0.2W = 0.8W.
Step 4: The area of the rectangle is given by the product of the length and the width, so the initial area is A = L * W.
Step 5: After the changes, the new area of the rectangle can be calculated using the new length and width, so the new area is A' = (2.2L) * (0.8W).
Step 6: Simplifying the new area, we get A' = 1.76LW.
Therefore, the area of the rectangle after the changes is 1.76 times the initial area. It has increased by 76%.
To determine what happens to the area of the rectangle when its length is increased by 120% and its width is decreased by 20%, we can follow these steps:
1. Let's assume the original length of the rectangle is L and the original width is W.
2. We calculate the new length by increasing the original length by 120%. This can be done by multiplying the original length (L) by 1 + (120% / 100) = 1.2.
New length = L * 1.2
3. We calculate the new width by decreasing the original width by 20%. This can be done by multiplying the original width (W) by 1 - (20% / 100) = 0.8.
New width = W * 0.8
4. Finally, we calculate the new area of the rectangle by multiplying the new length by the new width.
New area = New length * New width
= (L * 1.2) * (W * 0.8)
= 1.2L * 0.8W
= 0.96LW
Therefore, the area of the rectangle is decreased to 96% of the original area.