Longest pole that fits in a box 3 ft by 4 ft by 10 ft

Step by step

The question

Question: what is the longest pole that fits in a box 3 ft by 4 ft by 10 ft?

The longest thing that fits goes from a bottom corner to the top corner on the other side: the diagonal through the box.

1 Floor diagonal

First the floor.

Its diagonal d makes a right triangle with the sides 3 and 4.

Pythagoras: d squared is 3 squared plus 4 squared.

3 times 3 is 9.

4 times 4 is 16.

Together 25.

5 times 5 is 25.

So d is 5.

Careful!

We cannot just add the sides.

A diagonal is a short cut: Pythagoras, twice.

2 Diagonal of the box

Now a new right triangle stands up: the floor diagonal d, the height 10, and the diagonal D of the box.

Pythagoras again: D squared is d squared plus 10 squared.

d squared is 25.

10 times 10 is 100.

Together 125.

125 is not a square number.

A calculator gives 11.180, and so on.

To the nearest tenth, D is about 11.2 ft.

3 Check

Let's check: the two steps are the same as l squared plus w squared plus h squared.

9 plus 16 plus 100 is 125, the same D squared.

So the answer is right!

Let's look back.

First: floor diagonal.

Then: diagonal of the box.

Last: check.