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If the length of a rectangle is increased by 20% and the width is decreased by 1

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Question: If the length of a rectangle is increased by 20% and the width is decreased by 10%, what is the percentage change in the area?

Options:

  1. 8% increase
  2. 10% decrease
  3. 12% increase
  4. 2% decrease

Correct Answer: 2% decrease

Solution: 

Let the original length be L and width be W. The new length is 1.2L and the new width is 0.9W. The original area is LW and the new area is (1.2L)(0.9W) = 1.08LW. The percentage change in area is ((1.08LW - LW) / LW) * 100 = 8% increase.

If the length of a rectangle is increased by 20% and the width is decreased by 1

Practice Questions

Q1
If the length of a rectangle is increased by 20% and the width is decreased by 10%, what is the percentage change in the area?
  1. 8% increase
  2. 10% decrease
  3. 12% increase
  4. 2% decrease

Questions & Step-by-Step Solutions

If the length of a rectangle is increased by 20% and the width is decreased by 10%, what is the percentage change in the area?
  • Step 1: Define the original length of the rectangle as L and the original width as W.
  • Step 2: Calculate the new length after a 20% increase. The new length is 1.2 times the original length, so it is 1.2L.
  • Step 3: Calculate the new width after a 10% decrease. The new width is 0.9 times the original width, so it is 0.9W.
  • Step 4: Calculate the original area of the rectangle. The original area is length times width, which is LW.
  • Step 5: Calculate the new area using the new length and new width. The new area is (1.2L) times (0.9W), which equals 1.08LW.
  • Step 6: Find the change in area by subtracting the original area from the new area. The change in area is 1.08LW - LW, which equals 0.08LW.
  • Step 7: Calculate the percentage change in area. The percentage change is (change in area / original area) times 100, which is (0.08LW / LW) * 100 = 8%.
  • Percentage Change – Understanding how to calculate percentage changes in dimensions and areas.
  • Area of a Rectangle – Applying the formula for the area of a rectangle and how changes in dimensions affect it.
  • Multiplicative Effects – Recognizing how increases and decreases in dimensions multiply to affect overall area.
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