The problem involves finding the base $b$ of a triangle, given the following information:

• The height of the triangle is 5 units.
• The area of the triangle is $32.5 \, \text{units}^2$.

The formula for the area of a triangle is:

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

Substituting the given values:

$32.5 = \frac{1}{2} \times b \times 5$

Now, let's solve for $b$:

1. Multiply both sides by 2 to eliminate the fraction: $65 = b \times 5$

2. Divide both sides by 5 to solve for $b$: $b = \frac{65}{5} = 13$

Thus, the length of the base $b$ is 13 units.

Would you like more details or have any other questions?

Here are 5 related questions to expand on this:

1. How would the base $b$ change if the area was doubled but the height remained the same?
2. What would the height be if the area were the same but the base was 26 units?
3. How do you calculate the perimeter of this triangle, assuming it's a right triangle?
4. How does the area formula change for other polygons, like a trapezoid?
5. Can the Pythagorean theorem be used here to find the hypotenuse of the triangle?

Tip: For triangles, always ensure you correctly identify the base and height perpendicular to each other when using the area formula.