Question

A straw is placed inside a rectangular box that is 1 inches by 1 inches by 2 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

To find the length of the straw, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length 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 straw forms the hypotenuse of a right triangle with the two sides of the rectangular box. Let's call the length of the straw "x".

Using the Pythagorean theorem, we have:

x^2 = 1^2 + 1^2 + 2^2

x^2 = 1 + 1 + 4

x^2 = 6

Taking the square root of both sides, we get:

x = √6

Therefore, the length of the straw is √6 inches.