Right triangle legs 3, 4 Easy

The question

Question: find the longest side of a right triangle with legs 3 and 4.

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 = 3 and b = 4.

3 Work out the squares

3² means 3 times 3.

That is 9.

4² means 4 times 4.

That is 16.

Write the squares: 9 + 16 = c².

9 plus 16 is 25.

4 Take the square root

c² is 25.

So c times c is 25.

That means c is the square root of 25.

The square root of 25 is the positive number that times itself makes 25.

5 times 5 is 25.

So c = 5.

The missing side is 5.

5 Check

Let's check: put c = 5 back.

First a² + b².

Now c².

Both are 25.

So c = 5 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.

▶ Watch it solved

Right triangle leg 5 hypotenuse 13 Medium

The question

Question: find the missing side of a right triangle with leg 5 and longest side 13.

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 = 5 and c = 13.

3 Work out the squares

5² means 5 times 5.

That is 25.

13² means 13 times 13.

That is 169.

Write the squares: 25 + b² = 169.

4 Remove the 25

We want b² by itself.

The 25 is in the way.

To remove 25, we take away 25.

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.

25 and − 25 make zero.

Cross them out.

169 minus 25 is 144.

5 Take the square root

b² is 144.

So b times b is 144.

That means b is the square root of 144.

The square root of 144 is the positive number that times itself makes 144.

12 times 12 is 144.

So b = 12.

The missing side is 12.

6 Check

Let's check: put b = 12 back.

First a² + b².

Now c².

Both are 169.

So b = 12 is right!

Let's look back.

First: name the sides.

Then: put the numbers in.

Then: work out the squares.

Then: remove the 25.

Then: take the square root.

Last: check.

▶ Watch it solved

Right triangle leg 9 cm hypotenuse 41 cm Harder

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.

▶ Watch it solved