Question
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.
(1 point)
cm
We can use the Pythagorean Theorem to find the length of the diagonal of the prism.
The vertical edge joining the front and left sides represents the height of the prism, which is 12 centimeters.
The front base edge represents the width of the prism, which is 3 centimeters.
The right base edge represents the length of the prism, which is 4 centimeters.
We can consider the diagonal as the hypotenuse of a right triangle, where the width and height are the legs.
Using the Pythagorean Theorem, we have:
diagonal^2 = width^2 + height^2
diagonal^2 = 3^2 + 12^2
diagonal^2 = 9 + 144
diagonal^2 = 153
Taking the square root of both sides, we get:
diagonal = √153
So the length of the diagonal of the prism is approximately 12.37 centimeters.