Step by step
The question
Question: find the longest side of a right triangle with legs 3 and 4.
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 = 3 and b = 4.
3 Work out the squares
3² means 3 times 3.
That is 9.
4² means 4 times 4.
That is 16.
Write the squares: 9 + 16 = c².
9 plus 16 is 25.
4 Take the square root
c² is 25.
So c times c is 25.
That means c is the square root of 25.
The square root of 25 is the positive number that times itself makes 25.
5 times 5 is 25.
So c = 5.
The missing side is 5.
5 Check
Let's check: put c = 5 back.
First a² + b².
Now c².
Both are 25.
So c = 5 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.