3D Pythagorean Theorem
diagonal = d
---
width = w
height = h
length = |
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)
○20 inches, 20 inches, 27 inches
○20 inches, 21 inches, 26 inches
○ 21 inches, 24 inches, 26 inches
○23 inches, 24 inches, 25 inches
Let's use the Pythagorean Theorem to find the possible length, width, and height for the box.
According to the Pythagorean Theorem, d^2 = w^2 + h^2 + l^2
Given that d = 41.5 inches, we can calculate the length, width, and height for each of the options, and see which one satisfies the equation.
1. Option 1: 20 inches, 20 inches, 27 inches
d^2 = 20^2 + 20^2 + 27^2
d^2 = 400 + 400 + 729
d^2 = 1529
d = √1529
d ≈ 39.11 inches
2. Option 2: 20 inches, 21 inches, 26 inches
d^2 = 20^2 + 21^2 + 26^2
d^2 = 400 + 441 + 676
d^2 = 1517
d = √1517
d ≈ 38.94 inches
3. Option 3: 21 inches, 24 inches, 26 inches
d^2 = 21^2 + 24^2 + 26^2
d^2 = 441 + 576 + 676
d^2 = 1693
d = √1693
d ≈ 41.15 inches
4. Option 4: 23 inches, 24 inches, 25 inches
d^2 = 23^2 + 24^2 + 25^2
d^2 = 529 + 576 + 625
d^2 = 1730
d = √1730
d ≈ 41.59 inches
Among the given options, the possible length, width, and height for the box that would satisfy a diagonal of at least 41.5 inches is Option 4: 23 inches, 24 inches, 25 inches.