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).

pythagorean theorem formula

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, 
AB2 + BC2 = AC2
AC2 = 122 + 52
AC = (122 + 52)½ = (122 + 52)
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, 
PQ2 + QR2 = PR2
102 = QR2 + 82
QR = (102 - 82)½ = √(102 - 82)
QR = 6 cm                                                                                        

Answer: The length of QR is 6 cm.