Question

If you want the diagonal, d, to be at least 41.5 inches, what would be a possible length, width, and height for the box?

(1 point)
Responses

​​​​​​​21 inches, 24 inches, 26 inches
​​​​​​​ 21 inches, 24 inches, 26 inches

23 inches, 24 inches, 25 inches
23 inches, 24 inches, 25 inches

20 inches, 21 inches, 26 inches
20 inches, 21 inches, 26 inches

20 inches, 20 inches, 27 inches

Answer 1

To determine whether a box's diagonal meets the required minimum of 41.5 inches, we can use the formula for the diagonal \( d \) of a rectangular box (also known as a rectangular prism):

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

Where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.

We'll calculate the diagonal for each option:

1. **21 inches, 24 inches, 26 inches**:
\[
d = \sqrt{21^2 + 24^2 + 26^2} = \sqrt{441 + 576 + 676} = \sqrt{1693} \approx 41.2 \text{ inches}
\]
(Does not meet requirement)

2. **23 inches, 24 inches, 25 inches**:
\[
d = \sqrt{23^2 + 24^2 + 25^2} = \sqrt{529 + 576 + 625} = \sqrt{1730} \approx 41.6 \text{ inches}
\]
(Meets requirement)

3. **20 inches, 21 inches, 26 inches**:
\[
d = \sqrt{20^2 + 21^2 + 26^2} = \sqrt{400 + 441 + 676} = \sqrt{1517} \approx 38.0 \text{ inches}
\]
(Does not meet requirement)

4. **20 inches, 20 inches, 27 inches**:
\[
d = \sqrt{20^2 + 20^2 + 27^2} = \sqrt{400 + 400 + 729} = \sqrt{1529} \approx 39.1 \text{ inches}
\]
(Does not meet requirement)

From these calculations, the only option that has a diagonal of at least 41.5 inches is:

**23 inches, 24 inches, 25 inches**