Area of a given triangle is `x_1` square units. If the sides of this triangle be doubled, then the area of the new triangle becomes `x_2` square units. Find the percentage increase in area.

Options

A. `100%`
B. `200%`
C. `300%`
D. None of these

Answer

To find the percentage increase in the area of a triangle when its sides are doubled, we can follow these steps:

### Step 1: Understand the relationship between the sides and area of a triangle
The area of a triangle is proportional to the square of its sides. If the sides of the triangle are doubled, the area increases by the square of the factor by which the sides are increased.

### Step 2: Define the original area
Let the area of the original triangle be \( x_1 \) square units.

### Step 3: Calculate the new area after doubling the sides
If the sides of the triangle are doubled, the new area \( x_2 \) can be calculated as:
\[ x_2 = 4 \times x_1 \]
This is because when the sides are doubled (factor of 2), the area increases by \( 2^2 = 4 \).

### Step 4: Calculate the increase in area
The increase in area can be calculated as:
\[ \text{Increase in area} = x_2 - x_1 = 4x_1 - x_1 = 3x_1 \]

### Step 5: Calculate the percentage increase
The percentage increase in area is given by the formula:
\[ \text{Percentage Increase} = \left( \frac{\text{Increase in area}}{\text{Original area}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage Increase} = \left( \frac{3x_1}{x_1} \right) \times 100 = 3 \times 100 = 300\% \]

### Conclusion
The percentage increase in the area of the triangle when its sides are doubled is **300%**.

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