Question

The percentage increase in the area of a triangle if its each side is doubled will be:

• A. $ 200\% $
• B. $ 300\% $
• C. $ 400\% $
• D. None of these

Hint:

When each side of a triangle is doubled, the area increases by a factor of $ 4 $ because the area is proportional to the square of the side length. This corresponds to a $ 400\% $ increase in the area.

Answer 1

The Correct Option is C

Step 1: Relationship Between Side Length and Area.
If each side of a triangle is doubled, then the new area is: \[ \text{New Area} = (2)^2 \times \text{Original Area} = 4 \times \text{Original Area}. \] Step 2: Calculate Percentage Increase.
Percentage increase is: \[ \frac{\text{New Area} - \text{Original Area}}{\text{Original Area}} \times 100\% = \frac{4\text{Original Area} - \text{Original Area}}{\text{Original Area}} \times 100\% = 3 \times 100\% = 300\%. \] Step 3: Analyze the Options.
Option (1): \(200\%\) — Incorrect.
Option (2): \(300\%\) — Correct.
Option (3): \(400\%\) — Incorrect (this is total area, not increase).
Option (4): None of these — Incorrect. Step 4: Final Answer.
\[ \boxed{300\%} \]