"Pythagorean triple generator" is the stuff related to forming a right triangle for which the lengths of the three sides are created.

For example, a teacher wants to give a question to the students related to right triangle.

She wants to create a question like "Find the missing side of the right triangle".

But she does not know, how to fix the lengths of the other two sides which can meet the condition of right triangle.

Here is the idea.

We can use the following formulas to form a right triangle.

Hypotenuse = m² + n²

Leg = m² - n²

Leg = 2mn

And always **m > n**

In the above formulas, you can take any positive values for "m" and "n" to get the three sides of a right triangle with the condition m > n.

For example, let m = 3, n = 2

Then,

hypotenuse = m² + n² = 3² + 2² = 9 + 4 = 13

leg = m² - n² = 3² - 2² = 9 - 4 = 5

leg = 2mn = 2(3)(2) = 12

Now, we can check whether 13, 5, 12 be the three sides of the right angle triangle using Pythagorean theorem.

That is,

**square of hypotenuse = sum of the squares of other sides **

** 13² = 5**² + 12²

** 169 = 25** + 144

169 = 169

In this way, we will be able to create the lengths of three sides of a right triangle using the formulas given above.

**Example 1 : **

Using 5 and 6, create the lengths of three sides of a right triangle.

**Solution : **

Since m > n, we can take m = 6 and n = 5

Then, we have

Hypotenuse = m² + n² = 6² + 5² = 36 + 25 = 61

Leg = m² - n² = 6² - 5² = 36 - 25 = 11

Leg = 2mn = 2(6)(5) = 60

**Hence, the lengths of three sides of the right triangle are **

**61, 11 and 60**

Let us look at the next example on "Pythagorean triple generator"

**Example 2 : **

Using 4 and 3, create the lengths of three sides of a right triangle.

**Solution :**

Since m > n, we can take m = 4 and n = 3

Then, we have

Hypotenuse = m² + n² = 4² + 3² = 16 + 9 = 25

Leg = m² - n² = 4² - 3² = 16 - 9 = 7

Leg = 2mn = 2(4)(3) = 24

**Hence, the lengths of three sides of the right triangle are**

**25, 7 and 24**

Let us look at the next example on "Pythagorean triple generator"

**Example 3 : **

Using 1 and 2, create the lengths of three sides of a right triangle.

**Solution :**

Since m > n, we can take m = 2 and n = 1

Then, we have

Hypotenuse = m² + n² = 2² + 1² = 4 + 1 = 5

Leg = m² - n² = 2² - 1² = 4 - 1 = 3

Leg = 2mn = 2(2)(1) = 4

**Hence, the lengths of three sides of the right triangle are**

**5, 3 and 4**

Let us look at the next example on "Pythagorean triple generator"

**Example 4 : **

Using 6 and 7, create the lengths of three sides of a right triangle.

**Solution :**

Since m > n, we can take m = 7 and n = 6

Then, we have

Hypotenuse = m² + n² = 7² + 6² = 49 + 36 = 85

Leg = m² - n² = 7² - 6² = 49 - 36 = 13

Leg = 2mn = 2(7)(6) = 84

**Hence, the lengths of three sides of the right triangle are**

**85, 13 and 84**

Let us look at the next example on "Pythagorean triple generator"

**Example 5 : **

Using 11 and 6, create the lengths of three sides of a right triangle.

**Solution :**

Since m > n, we can take m = 11 and n = 6

Then, we have

Hypotenuse = m² + n² = 11² + 6² = 121 + 36 = 157

Leg = m² - n² = 11² - 6² = 121 - 36 = 85

Leg = 2mn = 2(11)(5) = 110

**Hence, the lengths of three sides of the right triangle are**

**157, 85 and 110**

After having gone through the stuff, we hope that the students would have understood "Pythagorean triple generator".

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