The problem asks to find the length of the base $b$ of the right triangle, given the area of the triangle and one side length.

Information provided:

• The area of the triangle is $\frac{3}{25}$ square centimeters.
• The height of the triangle (one leg) is $2.5$ cm.

Formula for the area of a triangle:

The area $A$ of a triangle is given by the formula: $A = \frac{1}{2} \times \text{base} \times \text{height}$ Substituting the values we know: $\frac{3}{25} = \frac{1}{2} \times b \times 2.5$

Now, let's solve for the base $b$.

Steps:

1. Multiply both sides by 2 to eliminate the fraction on the right side: $\frac{6}{25} = b \times 2.5$

2. Now, divide both sides by 2.5 to isolate $b$: $b = \frac{6}{25} \div 2.5$

I'll calculate this next.The length of the base $b$ of the triangle is $0.096$ cm.

Would you like more details on the steps, or do you have any other questions?

Here are some related questions:

1. How would the formula change if the area were given in different units?
2. What if the height of the triangle were doubled? How would that affect the base?
3. How can you express the base length as a fraction instead of a decimal?
4. What are some other methods to find the area of a triangle?
5. How does this formula apply to other types of triangles, not just right triangles?

Tip: In right triangles, knowing two dimensions (base, height) is often enough to solve for the third, like the area or hypotenuse.