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A rectangular prism is shown with the dimensions.



Question
What is the distance between A and D? Enter the answer in the box. Round the answer to the nearest hundredth of an inch.

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inches

Answer 1

To answer the question about the distance between points A and D in a rectangular prism, we need to know the coordinates or the specific dimensions of the prism.

If we assume points A and D are diagonally opposite corners of the rectangular prism, and we have the dimensions of the prism (length, width, height), we can find the distance using the 3D distance formula.

The formula to calculate the distance \(d\) between two points \((x_1, y_1, z_1)\) and \((x_2, y_2, z_2)\) in three-dimensional space is:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2} \]

If you provide the dimensions or coordinates of points A and D, I can calculate the exact distance for you. Please let me know those details!

Answer 2

7 in 24 in 10 in

Answer 3

To find the distance between points A and D in a rectangular prism with dimensions of 7 inches, 24 inches, and 10 inches, we assume that these dimensions correspond to the length, width, and height of the prism.

Let's assign coordinates to points A and D. If we consider A to be at the origin (0, 0, 0) and D to be at the opposite corner (7, 24, 10), we can use these coordinates for our calculation.

Using the distance formula for the diagonal:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2} \]

We plug in the coordinates:

• Point A (0, 0, 0)
• Point D (7, 24, 10)

Now, substituting the values:

\[ d = \sqrt{(7 - 0)^2 + (24 - 0)^2 + (10 - 0)^2} \] \[ d = \sqrt{7^2 + 24^2 + 10^2} \] \[ d = \sqrt{49 + 576 + 100} \] \[ d = \sqrt{725} \] \[ d \approx 26.9258 \]

Rounding to the nearest hundredth:

\[ d \approx 26.93 \text{ inches} \]

So, the distance between points A and D is 26.93 inches.