Question

A straw is placed in a rectangular box that is 6 inches by 4 inches by 8 inches, as shown. If the straw fits exactly in 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

$length=2\sqrt[]{29}$

Explanation

you can solve this by using the distance between 2 points formula

$D_{ab}=\sqrt[]{(x-x_1)^2+(y-y_1)^2+(z-z_1)^2}$

then

Step 1

Let

P1(0,0,0)

P2(6,4,8)

now , replace

$\begin{gathered} D_{ab}=\sqrt[]{(x-x_1)^2+(y-y_1)^2+(z-z_1)^2} \\ D_{ab}=\sqrt[]{(6-0)^2+(4-0)^2+(8-0)^2} \\ D_{ab}=\sqrt[]{(6)^2+(4)^2+(8)^2} \\ D_{ab}=\sqrt[]{36^{}+16+64} \\ D_{ab}=\sqrt[]{116} \\ D_{ab}=\sqrt[]{4\cdot29} \\ D_{ab}=2\sqrt[]{29} \end{gathered}$

I hope this helps you