Question

A straw is placed inside a rectangular box that is 3 inches by 7 inches by 6 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

3sqrt(5)

Explanation:

We can use the Pythagorean theorem to find the length of the diagonal of the rectangular box.

The Pythagorean theorem states that for a right triangle with legs of length a and b and hypotenuse of length c, we have:

c^2 = a^2 + b^2

In this case, the legs of the right triangle are 3 inches and 6 inches, and the hypotenuse is the length of the straw. So we have:

straw length^2 = 3^2 + 6^2 straw length^2 = 9 + 36 straw length^2 = 45

Taking the square root of both sides, we get:

straw length = sqrt(45) = sqrt(9*5) = sqrt(9)*sqrt(5) = 3sqrt(5)

Therefore, the length of the straw is 3sqrt(5) inches.