# Two sides of a triangle measure 5 in and 12 in which could be the length of the third side

## The Pythagorean Theorem

In a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. This is known as the Pythagorean Theorem and can be represented as: a^2 + b^2 = c^2.

### What is the Pythagorean Theorem?

The Pythagorean Theorem is a statement in mathematics that states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. In other words, c2 = a2 + b2.

### How is the Pythagorean Theorem used?

The Pythagorean Theorem is used in many different ways. One way is to find the hypotenuse of a right angled triangle when the other two sides are known. This is done by squaring both of the known sides and adding them together. Then the square root of this number is taken to give the hypotenuse.

## Applications of the Pythagorean Theorem

### Solving for the hypotenuse of a right triangle

To solve for the hypotenuse of a right triangle, you can use the Pythagorean Theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. In other words, if you know the lengths of two sides of a right triangle, you can use this theorem to find the length of the third side.

For example, let’s say you have a right triangle with sides that measure 5 inches and 12 inches. To find the length of the third side (the hypotenuse), you would need to use the following equation:

hypotenuse^2 = 5^2 + 12^2

You would then solve this equation to find that the length of the hypotenuse is 13 inches.

### Applying the Pythagorean Theorem to real-world scenarios

The Pythagorean Theorem is a statement in mathematics that states that in a right angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. This theorem is represented by the equation: a^2 + b^2 = c^2. The theorem is named after Greek mathematician Pythagoras, who is credited with discovering this relationship.

The theorem has many applications in the real world. Architects and engineers use it to determine the measurements of right angled triangles in their designs. It can be used to calculate distances, for example, in surveying or mapmaking. It also has applications in computer graphics and carpentry.