A rectangular prism is shown with its dimensions.

Question

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:

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