Step by step
The question
Question: find the missing side of a right triangle with leg 9 cm and longest side 41 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 = 9 and c = 41.
3 Work out the squares
9² means 9 times 9.
That is 81.
41² means 41 times 41.
That is 1681.
Write the squares: 81 + b² = 1681.
4 Remove the 81
We want b² by itself.
The 81 is in the way.
To remove 81, we take away 81.
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.
81 and − 81 make zero.
Cross them out.
1681 minus 81 is 1600.
5 Take the square root
b² is 1600.
So b times b is 1600.
That means b is the square root of 1600.
The square root of 1600 is the positive number that times itself makes 1600.
40 times 40 is 1600.
So b = 40 cm.
The missing side is 40 cm.
6 Check
Let's check: put b = 40 cm back.
First a² + b².
Now c².
Both are 1681.
So b = 40 cm is right!
Let's look back.
First: name the sides.
Then: put the numbers in.
Then: work out the squares.
Then: remove the 81.
Then: take the square root.
Last: check.