The problem asks for the length of the base $b$ of a triangle given its area and height.

We are given:

• The area of the triangle $A = \frac{25}{18}$ square meters.
• The height $h = \frac{5}{3}$ meters.

The formula for the area of a triangle is:

$A = \frac{1}{2} \times b \times h$

We can plug in the known values and solve for $b$.

$\frac{25}{18} = \frac{1}{2} \times b \times \frac{5}{3}$

Now let's solve for $b$. I'll calculate that for you.The length of the base $b$ is $\frac{5}{3}$ meters.

Would you like further details or have any questions?

Here are 5 related questions you might find useful:

1. How is the area of other geometric shapes calculated?
2. How would the formula change for an isosceles triangle?
3. Can you use this method to find the base if given the perimeter instead of the area?
4. What is the relationship between the height and base in right triangles?
5. How does the unit conversion affect the area formula?

Tip: Always express your answers in the simplest form for clarity and accuracy.