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The problem states the following:

"The height of a triangle is 1 meter less than the length of its base. The area of the triangular region is 28 m². Determine the length of the base and its height."

Let's break this down using algebra:

1. Let the base of the triangle be \( b \) (in meters).
2. Since the height is 1 meter less than the base, the height is \( b - 1 \) meters.
3. The formula for the area of a triangle is:

\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]

Substituting the values into the formula:

\[
28 = \frac{1}{2} \times b \times (b - 1)
\]

Simplifying:

\[
28 = \frac{1}{2} \times (b^2 - b)
\]
\[
56 = b^2 - b
\]
\[
b^2 - b - 56 = 0
\]

Now, we can solve this quadratic equation using the quadratic formula:

\[
b = \frac{-(-1) \pm \sqrt{(-1)^2 - 4 \times 1 \times (-56)}}{2 \times 1}
\]
\[
b = \frac{1 \pm \sqrt{1 + 224}}{2}
\]
\[
b = \frac{1 \pm \sqrt{225}}{2}
\]
\[
b = \frac{1 \pm 15}{2}
\]

This gives two possible solutions:

\[
b = \frac{1 + 15}{2} = 8 \quad \text{or} \quad b = \frac{1 - 15}{2} = -7
\]

Since the base cannot be negative, the base is \( b = 8 \) meters.

Finally, the height is:

\[
h = b - 1 = 8 - 1 = 7 \, \text{meters}
\]

### Solution:
- Base: \( 8 \) meters
- Height: \( 7 \) meters

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you apply the quadratic formula to solve for unknowns?
2. What other methods can be used to solve quadratic equations?
3. What are the conditions where a quadratic equation might have no real solution?
4. Can the area of other shapes, like parallelograms, be solved similarly?
5. How do you verify solutions in geometry problems?

**Tip:** Always check the dimensions of the variables to ensure the physical plausibility of the results (e.g., negative lengths).

La altura de un triángulo es 1 metro menos que la longitud de su base. El área de dicha región triangular es 28 m². Determina la medida de su base y su altura.

Learn how to solve for the base and height of a triangle, where the height is 1 meter less than the base, and the area is 28 m². Using the quadratic formula, this solution is suitable for students in Grades 8-10.

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