The area of a triangular window is given by the formula:

$A = \frac{1}{2} \times \text{base} \times \text{height}$

In this case, the area $A$ is 27.5 square meters, and the base is described as "2 meters shorter than twice the height." So, the base can be expressed as:

$\text{base} = 2h - 2$

Substituting these values into the area formula, we get:

$27.5 = \frac{1}{2} \times (2h - 2) \times h$

Now, you can use this equation to find the height $h$ of the window.

Would you like me to solve this equation for $h$ or provide more details?

Here are some related questions you might want to explore:

1. What is the value of $h$ when the equation is solved?
2. How would the area change if the height increased by 1 meter?
3. How does the base-to-height relationship affect the window's design?
4. Can this equation be solved graphically?
5. What are the units involved in solving the equation?

Tip: Always check the relationship between dimensions before solving, as it can help simplify the equation.