Step by step
The question
Question: find the missing side of a right triangle with leg 12 and longest side 20.
1 Name the sides
The longest side is called the hypotenuse.
We call it c.
It is always across from the right angle.
The two shorter sides make the right angle.
We call them a and b.
The rule for every right triangle: a² + b² = c².
2 Put the numbers in
Now put the numbers in: a = 12 and c = 20.
3 Work out the squares
12² means 12 times 12.
That is 144.
20² means 20 times 20.
That is 400.
Write the squares: 144 + b² = 400.
4 Remove the 144
We want b² by itself.
The 144 is in the way.
To remove 144, we take away 144.
We do it on both sides.
Why both sides?
The = sign means both sides are the same amount.
If we change only one side, they are not the same any more.
144 and − 144 make zero.
Cross them out.
400 minus 144 is 256.
5 Take the square root
b² is 256.
So b times b is 256.
That means b is the square root of 256.
The square root of 256 is the positive number that times itself makes 256.
16 times 16 is 256.
So b = 16.
The missing side is 16.
6 Check
Let's check: put b = 16 back.
First a² + b².
Now c².
Both are 400.
So b = 16 is right!
Let's look back.
First: name the sides.
Then: put the numbers in.
Then: work out the squares.
Then: remove the 144.
Then: take the square root.
Last: check.