Step by step
The question
Question: find the missing side of a right triangle with leg 2 and longest side 5.
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 c = 5.
3 Work out the squares
2² means 2 times 2.
That is 4.
5² means 5 times 5.
That is 25.
Write the squares: 4 + b² = 25.
4 Remove the 4
We want b² by itself.
The 4 is in the way.
To remove 4, we take away 4.
We do it on both sides.
Why both sides?
The = sign means both sides are the same amount.
If we change only one side, they are not the same any more.
4 and − 4 make zero.
Cross them out.
25 minus 4 is 21.
5 Take the square root
b² is 21.
So b times b is 21.
That means b is the square root of 21.
21 is not a square number.
So we keep √21.
That is the exact answer.
It is between 4 and 5.
With a calculator, √21 is about 4.6, to the nearest tenth.
So b is about 4.6.
6 Check
Let's check: put b = √21 back.
First a² + b².
Now c².
√21 times √21 is 21.
Both are 25.
So b = √21 is right!
Let's look back.
First: name the sides.
Then: put the numbers in.
Then: work out the squares.
Then: remove the 4.
Then: take the square root.
Last: check.