Use the image to answer the 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.
To find the length of the diagonal of the prism, we can use the Pythagorean theorem. The diagonal forms a right triangle with the height, width, and length of the prism.
The height of the prism is given as 12 centimeters.
The width of the prism is given as 3 centimeters.
The length of the prism is given as 4 centimeters.
Using the Pythagorean theorem, we can write the equation:
diagonal^2 = height^2 + width^2 + length^2
diagonal^2 = 12^2 + 3^2 + 4^2
diagonal^2 = 144 + 9 + 16
diagonal^2 = 169
Taking the square root of both sides, we get:
diagonal = √169
diagonal = 13 centimeters
Therefore, the length of the diagonal of the prism is 13 centimeters.