Diagonal of a box 6 by 8 by 24

Step by step

The question

Question: find the diagonal of a box 6 by 8 by 24.

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 6 and 8.

Pythagoras: d squared is 6 squared plus 8 squared.

6 times 6 is 36.

8 times 8 is 64.

Together 100.

10 times 10 is 100.

So d is 10.

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 24, and the diagonal D of the box.

Pythagoras again: D squared is d squared plus 24 squared.

d squared is 100.

24 times 24 is 576.

Together 676.

26 times 26 is 676.

So D = 26.

3 Check

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

36 plus 64 plus 576 is 676, the same D squared.

So the answer is right!

Let's look back.

First: floor diagonal.

Then: diagonal of the box.

Last: check.