Step by step
The question
Question: find the longest side of a right triangle with legs 2 cm and 3 cm.
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 = 2 and b = 3.
3 Work out the squares
2² means 2 times 2.
That is 4.
3² means 3 times 3.
That is 9.
Write the squares: 4 + 9 = c².
4 plus 9 is 13.
4 Take the square root
c² is 13.
So c times c is 13.
That means c is the square root of 13.
13 is not a square number.
So we keep √13.
That is the exact answer.
It is between 3 and 4.
With a calculator, √13 is about 3.6, to the nearest tenth.
So c is about 3.6 cm.
5 Check
Let's check: put c = √13 back.
First a² + b².
Now c².
√13 times √13 is 13.
Both are 13.
So c = √13 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.