A right triangular prism

has volume equal to 288
cm^3 . The height of the
prism is 3 cm. One of the
bases of the triangular
face (not the hypotenuse)
is equal to 12 cm,
determine the length of
the hypotenuse (in cm) of
the triangular face.

To determine the length of the hypotenuse of the triangular face of the right triangular prism, we need to know the lengths of the other two sides of the triangle.

First, let's calculate the area of the triangular base. The formula for the area of a triangle is:

Area = (1/2) * base * height

Given that the height is 3 cm and one of the bases is 12 cm, we can substitute these values into the formula:

Area = (1/2) * 12 cm * 3 cm = 18 cm^2.

Since the triangular face is a right triangle, we can also use the Pythagorean theorem to find the length of the hypotenuse. The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Let's assume that the other two sides of the right triangle are a and b, where a is the base of the triangle and b is the height of the triangle.

Using the Pythagorean theorem, we have the equation:

a^2 + b^2 = c^2

where c represents the length of the hypotenuse.

We know that a = 12 cm (given) and b = 3 cm (given). Substituting these values into the equation, we get:

12^2 + 3^2 = c^2
144 + 9 = c^2
153 = c^2

Now, we need to find the square root of both sides to determine the length of the hypotenuse:

c = √(153)

Using a calculator, we find that √(153) ≈ 12.37 cm.

Therefore, the length of the hypotenuse of the triangular face is approximately 12.37 cm.