Question

An illustration of a rectangular prism is shown with labeled parts. The top, front and right sides are visible. The bottom, left, and rear sides are not visible, but their positions are indicated by dashed lines. The vertical edge joining the front and left sides shows a height of 12 centimeters. The front base edge shows a width of 3 centimeters. The right base edge shows a length of 4 centimeters. A dotted line extends diagonally from the vertex at the bottom back right side of the prism through the interior of the prism to the vertex at the top front left.

Find the length of the diagonal of the prism.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the length of the diagonal of the prism, we need to use the Pythagorean theorem.

Let's consider the right triangle formed by the diagonal, the height, and the length of the prism.

Using the Pythagorean theorem, we have:

(diagonal)^2 = (height)^2 + (length)^2
(diagonal)^2 = (12 cm)^2 + (4 cm)^2
(diagonal)^2 = 144 cm^2 + 16 cm^2
(diagonal)^2 = 160 cm^2

Taking the square root of both sides, we get:
diagonal = √160 = √(16 x 10) = 4√10 cm

Therefore, the length of the diagonal of the prism is 4√10 centimeters.