Step by step
The question
Question: find the longest side of a right triangle with legs 4 and 7.
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 = 4 and b = 7.
3 Work out the squares
4² means 4 times 4.
That is 16.
7² means 7 times 7.
That is 49.
Write the squares: 16 + 49 = c².
16 plus 49 is 65.
4 Take the square root
c² is 65.
So c times c is 65.
That means c is the square root of 65.
65 is not a square number.
So we keep √65.
That is the exact answer.
It is between 8 and 9.
With a calculator, √65 is about 8.1, to the nearest tenth.
So c is about 8.1.
5 Check
Let's check: put c = √65 back.
First a² + b².
Now c².
√65 times √65 is 65.
Both are 65.
So c = √65 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.