Question: User: Triangle J is shown below. James drew a scaled version of Triangle J using a scale factor of 4 and labeled it Triangle K.
Triangle J
4
5
What is the area of Triangle K?
square units
Triangle J right triangle with a vertical left side labeled 4 and a horizontal bottom side labeled 5, located center-right. position_hint \in {center-right}
1. **State the problem:** We have Triangle J, a right triangle with legs of lengths $4$ and $5$. James created Triangle K by scaling Triangle J by a factor of $4$. We need to find the area of Triangle K.
2. **Formula for area of a right triangle:**
$$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$
3. **Calculate the area of Triangle J:**
$$\text{Area}_J = \frac{1}{2} \times 4 \times 5 = \frac{1}{2} \times 20 = 10$$
4. **Effect of scaling on area:**
When a figure is scaled by a factor of $k$, its area is scaled by a factor of $k^2$.
5. **Calculate the area of Triangle K:**
$$\text{Area}_K = k^2 \times \text{Area}_J = 4^2 \times 10 = 16 \times 10 = 160$$
6. **Final answer:**
The area of Triangle K is $160$ square units.