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.
20
To find the length of the hypotenuse of the triangular face, we need to use the volume and the dimensions of the prism.
First, let's visualize the right triangular prism. It has a triangular base and three rectangular faces. The height of the prism is given as 3 cm, and one of the bases of the triangular face is 12 cm.
The volume of a right triangular prism is given by the formula: Volume = (1/2) * base * height * length, where the base is the area of the triangular base and length is the length of the prism.
Given that the volume is 288 cm^3, the height is 3 cm, and the base is 12 cm, we can substitute the values into the volume formula:
288 cm^3 = (1/2) * 12 cm * 3 cm * length
Simplifying further:
288 cm^3 = 18 cm^2 * length
Now, let's solve for the length:
length = 288 cm^3 / 18 cm^2
length = 16 cm
Therefore, the length of the triangular face (hypotenuse) of the prism is 16 cm.