A triangle has an area of 129.5 square miles and a base of 18.5 miles. What is the height?

1. Break Down the Problem

To find the height of a triangle, we will use the formula for the area of a triangle: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ Here, we are given:

• Area = 129.5 square miles
• Base = 18.5 miles We need to find the height.

2. Relevant Concepts

We can rearrange the area formula to solve for height: $\text{height} = \frac{2 \times \text{Area}}{\text{base}}$

3. Analysis and Detail

Now, we'll substitute the known values into the rearranged formula: $\text{height} = \frac{2 \times 129.5}{18.5}$

4. Verify and Summarize

Calculating the height:

1. Calculate $2 \times 129.5$: $2 \times 129.5 = 259$

2. Now divide by the base: $\text{height} = \frac{259}{18.5} \approx 14$

Final Answer

The height of the triangle is approximately $14$ miles.