If a rectangle's length is doubled and its width is halved, what happens to its

₹0.0

Question: If a rectangle\'s length is doubled and its width is halved, what happens to its area?

Options:

Correct Answer: It doubles

Solution:

New area = (2 * length) * (width/2) = length * width = original area, so it doubles.

If a rectangle's length is doubled and its width is halved, what happens to its area?

If a rectangle's length is doubled and its width is halved, what happens to its area?

Step 1: Understand the formula for the area of a rectangle, which is Area = Length * Width.
Step 2: Let the original length be 'L' and the original width be 'W'. So, the original area is A = L * W.
Step 3: Now, if the length is doubled, the new length becomes '2L'.
Step 4: If the width is halved, the new width becomes 'W/2'.
Step 5: Calculate the new area using the new dimensions: New Area = (2L) * (W/2).
Step 6: Simplify the new area: New Area = 2L * (W/2) = (2L * W) / 2 = L * W.
Step 7: Compare the new area to the original area: New Area = L * W, which is the same as the original area.
Step 8: Therefore, the area does not change; it remains the same.

Area of a Rectangle – The area of a rectangle is calculated by multiplying its length by its width.
Effect of Dimensional Changes – Understanding how changes in dimensions (doubling length and halving width) affect the overall area.