If the length of an object is doubled, what happens to its area?
Correct Answer: Area increases by a factor of four.
- Step 1: Understand that area is calculated using the formula A = length × width.
- Step 2: If we only consider a square or rectangle, we can say that both the length and width are the same (length = width).
- Step 3: If the length of the object is doubled, we can represent the new length as 2 × length.
- Step 4: The new area will be calculated as A = (2 × length) × (2 × length).
- Step 5: Simplifying this, we get A = 4 × (length × length) = 4 × original area.
- Step 6: Therefore, when the length is doubled, the area increases by a factor of four.
- Area Calculation – Understanding that area is calculated as length squared (A = length²) and how changes in dimensions affect area.
