Step by step
The question
Question: find the longest side of a right triangle with legs 8 cm and 15 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 = 8 and b = 15.
3 Work out the squares
8² means 8 times 8.
That is 64.
15² means 15 times 15.
That is 225.
Write the squares: 64 + 225 = c².
64 plus 225 is 289.
4 Take the square root
c² is 289.
So c times c is 289.
That means c is the square root of 289.
The square root of 289 is the positive number that times itself makes 289.
17 times 17 is 289.
So c = 17 cm.
The missing side is 17 cm.
5 Check
Let's check: put c = 17 cm back.
First a² + b².
Now c².
Both are 289.
So c = 17 cm 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.