Question

A straw is placed inside a rectangular box that is 6 inches by 2 inches by 4 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in simplest radical form.

Answer 1

The length of the straw is sqrt(56) inches.

Step-by-step explanation:

To find the length of the straw, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the length and width of the rectangular box represent the legs of the right triangle, and the diagonal of the box is the hypotenuse.

We can calculate the length of the diagonal using the formula:
diagonal = sqrt(length^2 + width^2 + height^2)

Substituting the given values, we get:
diagonal = sqrt(6^2 + 2^2 + 4^2) = sqrt(36 + 4 + 16) = sqrt(56)

Since the question asks for the length in simplest radical form, the length of the straw is sqrt(56) inches.