Perimeter of Right Triangle

• Perimeter is the distance around the outside of a shape.
• It is measured as a length and can be in a range of units such as cm, inches, feet, miles, etc.

When we are trying to find the perimeter of a right triangle, there are several different ways we can do this.

Which way you select will depend on several factors, such as whether the shape is drawn to scale and whether the side lengths are given.

This is the easiest example to deal with.

• All you need to do to find the perimeter of right triangle is to add up the three side lengths.

Examples

Example 1

In the example above, we just need to add up the lengths of the three sides:

3cm + 4cm + 5cm = 12cm.

So the perimeter of right triangle is 12cm.

This is another straightforward example to work out.

• All you need to do is to use a ruler, measure the sides and add up the length of each of the sides.

Note that you will often end up with a decimal answer for your perimeter.

To work this out, we need to use Pythagoras' theorem to find the longest side and then add on the lengths of the other two sides.

• Use Pythagoras' theorem to find the length of the longest side and then add on the lengths of the other two sides.

Examples

Example 1 (not drawn to scale)

Pythagoras' theorem says that the square of the two shorter sides on a right triangle is equal to the square of the longest side (the hypotenuse).

So if h is the longest side (or hypotenuse), then h² = 6² + 3².

This gives us that h² = 36 + 9 = 45

So h must equal √45 which is equal to 6.71 to 2dp.

The next step is to add up the lengths of all the sides.

6.71cm + 6cm + 3cm = 15.71cm

So the perimeter of the right triangle is 15.71cm to 2dp.

Example 2 (not drawn to scale)

Using Pythagoras' theorem again.

So if h is the longest side (or hypotenuse), then h² = 4² + 4².

This gives us that h² = 16 + 16 = 32

So h must equal √32 which is equal to 5.66 to 2dp.

The next step is to add up the lengths of all the sides.

5.66cm + 4cm + 4cm = 13.66cm

So the perimeter of the right triangle is 13.66cm to 2dp.

To work this out, we need to use Pythagoras' theorem to find the shorter side (or leg) that is missing and then add on the lengths of the other two sides.

• Use Pythagoras' theorem to find the length of the leg and then add on the lengths of the other two sides.

Examples

Example 1 (not drawn to scale)

Find the perimeter of right triangle below.

Pythagoras' theorem says that the square of the two shorter sides (legs) on a right triangle is equal to the square of the longest side (the hypotenuse).

So if s is the leg that is missing, then s² + 5² = 8².

So s² + 25 = 64

This means that s² = 64 - 25 = 39

So s = √39 = 6.24cm to 2dp.

The next step is to add up all the sides.

6.24cm + 5cm + 8cm = 19.24cm.

So the perimeter of the right triangle is 19.24cm to 2dp.

Example 2 (not drawn to scale)

Pythagoras' theorem says that the square of the two shorter sides on a right triangle is equal to the square of the longest side (the hypotenuse).

So if s is the leg that is missing, then s² + 6² = 10².

So s² + 36 = 100

This means that s² = 100 - 36 = 64

So s = √64 = 8cm.

The next step is to add up all the sides.

8cm + 6cm + 10cm = 24cm.

So the perimeter of the right triangle is 24cm.

If you would like to practice these skills yourself, why not try our worksheets all about finding the perimeter of a right triangle.

The first sheet involves measuring with a ruler only.

The second sheet involves using Pythagoras' theorem (whole number answers only)

The third and fourth sheets involve finding the perimeters of right triangles using Pythagoras' theorem with answers to 1dp.

We have a selection of perimeter help and support as well as perimeter worksheets.

The perimeter worksheets are all graded in order from easiest to hardest.

Using these sheets will help your child to:

• work out the perimeter of a range of rectangles;
• find the perimeter of rectilinear shapes.

The area sheets are all graded in order from easiest to hardest.

Using these sheets will help your child to:

• work out the areas of a range of rectangles;
• find the area of rectilinear shapes.

All the sheets in this section support Elementary Math Benchmarks.

Another way to learn about 'What does perimeter mean' is through exploring shapes.

This online area and perimeter activity by toytheater.com will let you explore 'what does perimeter mean' through creating your own shapes.

The link below will open in a new browser window.

The Math Salamanders hope you enjoy using these free printable Math worksheets and all our other Math games and resources.

We welcome any comments about our site or worksheets on the Facebook comments box at the bottom of every page.