Diagonal of a box 1 by 2 by 2

Step by step

The question

Question: find the diagonal of a box 1 by 2 by 2.

The diagonal goes from a bottom corner to the top corner on the other side, right through the box.

1 Floor diagonal

First the floor.

Its diagonal d makes a right triangle with the sides 1 and 2.

Pythagoras: d squared is 1 squared plus 2 squared.

1 times 1 is 1.

2 times 2 is 4.

Together 5.

5 is not a square number.

We do not need d itself: the next step uses d squared.

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 2, and the diagonal D of the box.

Pythagoras again: D squared is d squared plus 2 squared.

d squared is 5.

2 times 2 is 4.

Together 9.

3 times 3 is 9.

So D = 3.

3 Check

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

1 plus 4 plus 4 is 9, the same D squared.

So the answer is right!

Let's look back.

First: floor diagonal.

Then: diagonal of the box.

Last: check.