Question

A rectangular prism is shown with its dimensions.



A rectangular prism.Short description, A rectangular prism.,Long description,
The rectangular prism has segment P Q that connects two opposite corners. The rectangular prism is 12 centimeters long, 9 centimeters wide, and 18 centimeters tall. Point P is the bottom-left back corner. Point Q is the top-right front corner. Segment P Q, labeled d, is a diagonal from the bottom-left back corner up through the prism to the top-right front corner.


Question
What is the distance, d, between P and Q? Round the answer to the nearest tenth. Enter the answer in the box.

Response area with 1 text input box
centimeters

Answer 1

To find the distance \( d \) between points \( P \) and \( Q \) in a rectangular prism, we can use the 3D distance formula, which is given by:

\[
d = \sqrt{l^2 + w^2 + h^2}
\]

where \( l \) is the length, \( w \) is the width, and \( h \) is the height of the prism.

Given:
- Length (\( l \)) = 12 cm
- Width (\( w \)) = 9 cm
- Height (\( h \)) = 18 cm

Now, we can substitute these values into the formula:

\[
d = \sqrt{(12)^2 + (9)^2 + (18)^2}
\]
\[
d = \sqrt{144 + 81 + 324}
\]
\[
d = \sqrt{549}
\]

Now, calculate \( \sqrt{549} \):

\[
d \approx 23.4
\]

Rounding to the nearest tenth, the distance \( d \) between points \( P \) and \( Q \) is:

\[
\boxed{23.4} \text{ centimeters}
\]