Perimeter of right angle triangle

In this tutorial, we will learn how to calculate the perimeter of a right angle triangle. A right angle triangle is a triangle that has one angle equal to 90 degrees. The perimeter of a triangle is the sum of the lengths of its three sides.

Calculating the Perimeter of a Right Angle Triangle

To calculate the perimeter of a right angle triangle, we will follow these steps:

Step 1: Identify the given side lengths

In a right angle triangle, you are usually given the lengths of two sides: the base (b) and the height (h), which are the two legs adjacent to the right angle. If you are given the length of the hypotenuse (c), you can use the Pythagorean theorem to find the lengths of the other two sides.

Step 2: Apply the Pythagorean theorem (if necessary)

The Pythagorean theorem states that in a right angle triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (b and h). Mathematically, it can be represented as:

c^2 = b^2 + h^2

If you are given the lengths of the base and height, you can use this theorem to calculate the length of the hypotenuse.

Step 3: Calculate the perimeter

Once you have the lengths of all three sides, simply add them together to find the perimeter of the right angle triangle:

Perimeter (P) = b + h + c

Now let’s see an example to better understand the process.

Example: Calculating the Perimeter of a Right Angle Triangle

Suppose we have a right angle triangle with a base (b) of 5 units and a height (h) of 12 units. We will follow the steps outlined above to calculate the perimeter.

Step 1: Identify the given side lengths

In this example, we are given the lengths of the base (b) and height (h):

b = 5 units h = 12 units

Step 2: Apply the Pythagorean theorem

We will use the Pythagorean theorem to find the length of the hypotenuse (c):

c^2 = b^2 + h^2 c^2 = (5)^2 + (12)^2 c^2 = 25 + 144 c^2 = 169 c = √169 c = 13 units

So, the length of the hypotenuse is 13 units.

Step 3: Calculate the perimeter

Now that we have the lengths of all three sides, we can calculate the perimeter:

Perimeter (P) = b + h + c P = 5 + 12 + 13 P = 30 units

The perimeter of the right angle triangle is 30 units.

Conclusion

In conclusion, calculating the perimeter of a right angle triangle involves identifying the given side lengths, applying the Pythagorean theorem if necessary, and adding the lengths of all three sides together. By following these steps, you can easily find the perimeter of any right angle triangle.