# Pythagorean Theorem Formula

Pythagoras theorem formula was introduced by the Greek Mathematician Pythagoras of Samos. This theorem gives the fundamental aspect in Euclidean Geometry connecting the three sides of a triangle provided the triangle must be right-angled. Let's learn about the Pythagorean theorem formula with a few solved examples in the end.

## What Is the Pythagorean Theorem Formula?

As per the Pythagorean theorem formula, in a right-angled triangle, the square of the hypotenuse side is equal to the sum of the square of the other two sides (that is adjacent and opposite sides).

## Solved Examples Using Pythagorean Theorem Formula

### Example 1:

A right-angled triangle ABC, has base BC = 12 cm, height AB = 5 cm. What is the length of AC?

**Solution:**

By Pythagoras Theorem we know that,

AB^{2} + BC^{2} = AC^{2}

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

AC = (12^{2} + 5^{2})^{½} = **√**(12^{2} + 5^{2})

AC = 13 cm

**Answer: The length of AC is 13 cm.**

### Example 2:

A right-angled triangle PQR, has angle Q = 90°. PQ = 8 cm. PR = 10 cm. Find QR.

**Solution:**

By Pythagoras Theorem we know that,

PQ^{2} + QR^{2} = PR^{2}

10^{2} = QR^{2} + 8^{2}

QR = (10^{2} - 8^{2})^{½} = √(10^{2} - 8^{2})

QR = 6 cm** **

**Answer: The length of QR is 6 cm.**

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