Step by step
The question
Question: find the longest side of a right triangle with legs 10 and 24.
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 = 10 and b = 24.
3 Work out the squares
10² means 10 times 10.
That is 100.
24² means 24 times 24.
That is 576.
Write the squares: 100 + 576 = c².
100 plus 576 is 676.
4 Take the square root
c² is 676.
So c times c is 676.
That means c is the square root of 676.
The square root of 676 is the positive number that times itself makes 676.
26 times 26 is 676.
So c = 26.
The missing side is 26.
5 Check
Let's check: put c = 26 back.
First a² + b².
Now c².
Both are 676.
So c = 26 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.