## Understanding the Pythagorean Theorem

**in a right-angled triangle, the square root of the side opposite the right angle (known as the hypotenuse) is equal to the sum of the squares of the other two sides.**The formula to represent this rule is

*a*. In this formula, 'a' and 'b' are the lengths of the other two sides of the triangle and are equal to the hypotenuse.

^{2}+b^{2}=c^{2}### 1

In right triangles (a triangle that is right sided), if one side is 3 units and the other side is 4 units, what is the length of the hypotenuse?

*a*. Here, 'a' and 'b' represent the lengths of the legs of the right-angled triangle, and 'c' is the length of the hypotenuse. To understand this in a practical sense, imagine measuring a physical object's dimensions or calculating the diagonal screen size of a television.

^{2}+b^{2}=c^{2}### 2

If the hypotenuse of a right-angled triangle is 13 units and one of the sides is 5 units, what is the length of the other side?

## Real-life applications of Pythagoras Theorem

### 3

If a graphic designer is creating a 3D model of a room that is 10 meters long and 8 meters wide, what would be the diagonal distance from one corner of the room to the opposite corner?

## Learn to use Pythagoras theorem formula for Maths GCSE

### 4

In a composite shape made of two right-angled triangles, if one triangle has sides of 3 cm and 4 cm, and the other has sides of 5 cm and 12 cm, what is the sum of the two lengths of the hypotenuses of both triangles?

### 5

In a scenario where a right-angled triangle has sides of 7 cm and 24 cm, what is the length of the hypotenuse?

## Applying Pythagoras Theorem in GCSE Maths

### 6

In a three-dimensional problem, if a rectangular box has a length of 8 cm, a width of 6 cm, and a height of 10 cm, find the unknown length of the diagonal running from one corner of the base to the opposite corner on the top?

## Beyond Pythagoras: Exploring advanced mathematical concepts

## Frequently asked questions

*c*, where 'c' is the hypotenuse and 'a' and 'b' are the other two sides of the triangle.

^{2}=a^{2}+b^{2}*c*to find the length of the unknown side, whether it is the hypotenuse or one of the other two sides.

^{2}=a^{2}+b^{2}## Final thoughts on Pythagoras Theorem

*This post was updated on 30 Nov, -0001.*