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

20 inches, 20 inches, 27 inches
20 inches, 20 inches, 27 inches

​​​​​​​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

Answer 1

To determine if the diagonal \( d \) of a box with given dimensions (length \( l \), width \( w \), and height \( h \)) is at least 41.5 inches, we can use the formula for the diagonal of a rectangular box:

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

We need to check each of the provided dimension sets to see if their diagonal is at least 41.5 inches.

1. **20 inches, 20 inches, 27 inches**:
\[
d = \sqrt{20^2 + 20^2 + 27^2} = \sqrt{400 + 400 + 729} = \sqrt{1529} \approx 39.1 \text{ inches}
\]

2. **21 inches, 24 inches, 26 inches**:
\[
d = \sqrt{21^2 + 24^2 + 26^2} = \sqrt{441 + 576 + 676} = \sqrt{1693} \approx 41.2 \text{ inches}
\]

3. **23 inches, 24 inches, 25 inches**:
\[
d = \sqrt{23^2 + 24^2 + 25^2} = \sqrt{529 + 576 + 625} = \sqrt{1730} \approx 41.6 \text{ inches}
\]

4. **20 inches, 21 inches, 26 inches**:
\[
d = \sqrt{20^2 + 21^2 + 26^2} = \sqrt{400 + 441 + 676} = \sqrt{1517} \approx 39.0 \text{ inches}
\]

From these calculations, the only set of dimensions that gives a diagonal of at least 41.5 inches is **23 inches, 24 inches, 25 inches** (with a diagonal of approximately 41.6 inches).

Thus, a possible length, width, and height for the box that meets the criteria is:

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