Find X in a Right Triangle: Given Area 8.375 and Height 2.5

To solve this problem, let's follow these steps:

• Step 1: Identify the given information: The area $A = 8.375$, one side $a = X$, and the other side $b = 2.5$.
• Step 2: Utilize the formula for the area of a right triangle, $A = \frac{1}{2} \times \text{base} \times \text{height}$.
• Step 3: Plug in the known values to the formula and solve for $X$.

Detailed solution:

We have the area formula for a right triangle:

$A = \frac{1}{2} \times X \times 2.5$

Substitute the given area value:

$8.375 = \frac{1}{2} \times X \times 2.5$

Let's rearrange this equation to solve for $X$:

$X = \frac{8.375 \times 2}{2.5}$

Calculate:

$X = \frac{16.75}{2.5} = 6.7$

Therefore, the length of side $X$ is $\mathbf{6.7}$.

This corresponds to choice 2: 6.7