To find the maximum possible area of a triangle with a given sum of the base and altitude, we can use the formula for the area of a triangle: Area = 1/2 * base * altitude.

Since the sum of the base and altitude is 30 cm, let`s assume the base is x cm. This means the altitude will be (30 - x) cm.

Substituting these values into the formula, we get:

Area = 1/2 * x * (30 - x)

Area = 15x - 1/2x^2

To find the maximum possible area, we need to find the vertex of the parabola given by the equation. The vertex is given by the formula x = -b/2a.

In this case, a = -1/2, and b = 15, so the x-coordinate of the vertex is x = -15 / (2 * (-1/2)) = 15.

Plugging this value of x into the equation, we can find the maximum area:

Area = 15(15) - 1/2(15^2) = 225 - 1/2(225) = 112.5 cm^2.

Therefore, the maximum possible