Pythagorean theorem

The Pythagorean Theorem was named after famous Greek mathematician Pythagoras.

It is an important formula that states the following:

In any right triangle,

Let c be the length of the longest side, called hypotenuse

Let a and b be the length of the other two sides, called legs

The theorem states that the length of the hypotenuse squared is equal to the length of side a squared and the length of side b squared

Written as an equation,

c2 = a2 + b2

Thus, given two sides, the third side can be found using the formula

We will illustrate with examples

Before proceeding, you should know How to find the square root of a number and how to solve equations using subtraction

Exercises #1

Let a = 3 and b = 4. Find c, or the longest side

c2 = a2 + b2

c2 = 32 + 42

c2= 9 + 16

c2 = 25

c = √25

The sign (√) means square root

c = 5

Exercises #2 Let c = 10 and a = 8. Find b, or the other leg.

c2 = a2 + b2

102 = 82 + b2

100 = 64 + b2

100 - 64 = 64 - 64 + b2 (minus 64 from both sides to isolate b2 )

36 = 0 + b2

36 = b2

b = √36 = 6

Let c = 13 and b = 5. Find a

c2 = a 2+ b2

132 = a2 + 52

169 = a2 + 25

169 - 25 = a2 + 25-25

144 = a2 + 0

144 = a2

a = √144 = 12

Take the Pythagorean theorem quiz below to see how well you understand this lesson.

Buy a comprehensive geometric formulas ebook. All geometric formulas are explained with well selected word problems.

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