If the dimensions of a \( 3-4-5 \) right triangle are increased \( 50 \% \), by what percent is the area increased?

The area of a right triangle is calculated using the formula \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \). For a \( 3-4-5 \) triangle, the area is \( \frac{1}{2} \times 3 \times 4 = 6 \). When the dimensions are increased by \( 50\% \), the new dimensions become \( 4.5 \) (which is \( 3 \times 1.5 \)) and \( 6 \) (which is \( 4 \times 1.5 \)). The new area is \( \frac{1}{2} \times 4.5 \times 6 = 13.5 \). To find the percent increase in the area: \[ \text{Percent Increase} = \frac{\text{New Area} - \text{Original Area}}{\text{Original Area}} \times 100 = \frac{13.5 - 6}{6} \times 100 = \frac{7.5}{6} \times 100 \approx 125\% \] So, the area increases by \( 125\% \).