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

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?

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.