Step by step
The question
Question: find the longest side of a right triangle with legs 20 m and 21 m.
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 = 20 and b = 21.
3 Work out the squares
20² means 20 times 20.
That is 400.
21² means 21 times 21.
That is 441.
Write the squares: 400 + 441 = c².
400 plus 441 is 841.
4 Take the square root
c² is 841.
So c times c is 841.
That means c is the square root of 841.
The square root of 841 is the positive number that times itself makes 841.
29 times 29 is 841.
So c = 29 m.
The missing side is 29 m.
5 Check
Let's check: put c = 29 m back.
First a² + b².
Now c².
Both are 841.
So c = 29 m 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.