Why does tripling the side lengths of a right triangle affect its area?

Answer 1

Tripling the side lengths of a right triangle increases its area by a factor of nine. The area of a triangle is calculated using the formula ( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} ). When the base and height are both tripled, the new area becomes ( \frac{1}{2} \times (3 \times \text{base}) \times (3 \times \text{height}) = 9 \times \text{Area} ). Thus, the area grows by the square of the scale factor applied to the side lengths.