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, we can use the formula for the volume of a right triangular prism. The formula is:
Volume = (1/2) * base * height * length
In this case, we know that the volume is 288 cm^3, the height is 3 cm, and one of the bases is 12 cm. Let's call the length of the hypotenuse "c". We need to solve for "c".
Therefore, the equation becomes:
288 = (1/2) * 12 * 3 * c
Simplifying the equation:
288 = 6 * 3 * c
288 = 18c
Dividing both sides by 18:
288 / 18 = c
16 = c
So, the length of the hypotenuse of the triangular face is 16 cm.