Step by step
The question
Question: find the longest side of a right triangle with legs 9 and 12.
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 = 9 and b = 12.
3 Work out the squares
9² means 9 times 9.
That is 81.
12² means 12 times 12.
That is 144.
Write the squares: 81 + 144 = c².
81 plus 144 is 225.
4 Take the square root
c² is 225.
So c times c is 225.
That means c is the square root of 225.
The square root of 225 is the positive number that times itself makes 225.
15 times 15 is 225.
So c = 15.
The missing side is 15.
5 Check
Let's check: put c = 15 back.
First a² + b².
Now c².
Both are 225.
So c = 15 is right!
Let's look back.
First: name the sides.
Then: put the numbers in.
Then: work out the squares.
Then: take the square root.
Last: check.