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------------------------------------------------ A triangle has an area of 38.4 square centimeters. The height of the triangle is 12.8 centimeters. What is the length of the base of the triangle?

To find the length of the base of a triangle given its area and height, we can use the formula for the area of a triangle:

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

Rearranging the formula to solve for the base, we get:

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

Given:
- Area of the triangle = 38.4 square centimeters
- Height of the triangle = 12.8 centimeters

Now, let's plug these values into the equation:

[tex]\[ \text{base} = \frac{2 \times 38.4}{12.8} \][/tex]

First, multiply the area by 2:

[tex]\[ 2 \times 38.4 = 76.8 \][/tex]

Then, divide this result by the height:

[tex]\[ \text{base} = \frac{76.8}{12.8} = 6 \][/tex]

So, the length of the base of the triangle is 6 centimeters.