A theorem that is accredited to Pythagoras that the square on the hypotenuse of any right-angled triangle is equal in area to the sum of the squares on the other two sides. It is called the Pythagoras theorem.

The formula goes like,

*a ^{2} + b^{2}= c^{2 }*

Where ‘a’ is the height, ‘b’ is the base & ‘c’ is the hypotenuse.

## Why Is It Useful?

When you have a right-angled triangle, and the length of all the three sides are not mentioned, then you can find one with the help of the other two. Thanks to Pythagoras that we can solve our problems easily with this formula & a bit of algebra. This combination is sure to give you the correct results.

## How To Use It?

Write it down as an equation that is,

*a ^{2} + b^{2}= c^{2 }*

Then apply algebra, to find out the missing value. Every kid is taught this magic theorem in their middle school period.

Let’s get into some demonstration.

Suppose that we have a right-angled triangle with a height of 5cms & base of 12cms. We need to find out the length of the hypotenuse of the triangle.

Step 1: **Apply the equation**

*a ^{2} + b^{2}= c^{2}*

Step 2: **Place The Values**

5^{2}+12^{2}=c^{2}

Step 3: **Calculate The Squares**

25+144=c^{2}

169=c^{2}

Step 4: **Swap The Sides**

c^{2}=169

Step 5: **Use Square Root On Both Sides And Get The Final Result**

c= √169

c=13

Therefore the length of the Hypotenuse is 13cms.

**Types Of Problems You Can Solve Using Pythagoras Theorem**

- Use it to find the length of the sides of any right-angled triangle.
- To find the length of the diagonal of a square. (because you know that every square is made up of 2 triangles).
- To prove that the given triangle is right-angled.
- To find if a triangle at all has a right angle or not.

## Conclusion

The Pythagoras theorem is an integral part of our mathematical grooming. It makes our experience with the right-angled triangles much easier and smooth. Therefore, it must be there in your curriculum.