Solve for X in Right Triangle: Given Area 22.5 and Side X+6

To solve this problem, we need to determine $X$ using the triangle area formula. Let's break it down step-by-step:

• Step 1: The area of a triangle $\Delta ABC$ is given by: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$
• Step 2: We substitute the given values where the base is $(X + 6)$ and the height is $5$: $22.5 = \frac{1}{2} \times (X + 6) \times 5$
• Step 3: Simplify the equation: $22.5 = \frac{1}{2} \times 5 \times (X + 6)$
• Step 4: Multiply out the constants: $22.5 = \frac{5}{2} \times (X + 6)$
• Step 5: Clear the fraction by multiplying both sides by 2: $45 = 5 \times (X + 6)$
• Step 6: Divide both sides by 5: $9 = X + 6$
• Step 7: Solve for $X$: $X = 9 - 6 = 3$

Therefore, the solution to the problem is $X = 3$.