Question

Kylie needs to pack her baton for a color-guard competition. The baton is 11 inches long. She has a rectangular box with a base of 6 inches by 8 inches and a height of 6 inches.

PART A: Could the baton lie flat on a diagonal along the base of the box? Explain.

PART B: Could the baton fit along the interior diagonal of the box? Explain.

Answer 1

Explanation:

PART A:

No, the baton cannot lie flat on a diagonal along the base of the box. The diagonal of the base can be found using the Pythagorean theorem as follows:

d = sqrt(6^2 + 8^2)

d = sqrt(36 + 64)

d = sqrt(100)

d = 10

The diagonal of the base is 10 inches, which is less than the length of the baton (11 inches). Therefore, the baton cannot lie flat on the diagonal of the base.

PART B:

Yes, the baton could fit along the interior diagonal of the box. The interior diagonal can be found using the Pythagorean theorem as follows:

d = sqrt(6^2 + 8^2 + 6^2)

d = sqrt(36 + 64 + 36)

d = sqrt(136)

d ≈ 11.66

The interior diagonal of the box is approximately 11.66 inches, which is greater than the length of the baton (11 inches). Therefore, the baton could fit along the interior diagonal of the box.