Step by step
The question
Question: find the longest side of a right triangle with legs 15 and 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 = 15 and b = 20.
3 Work out the squares
15² means 15 times 15.
That is 225.
20² means 20 times 20.
That is 400.
Write the squares: 225 + 400 = c².
225 plus 400 is 625.
4 Take the square root
c² is 625.
So c times c is 625.
That means c is the square root of 625.
The square root of 625 is the positive number that times itself makes 625.
25 times 25 is 625.
So c = 25.
The missing side is 25.
5 Check
Let's check: put c = 25 back.
First a² + b².
Now c².
Both are 625.
So c = 25 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.