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,
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
Let a = 3 and b = 4. Find c, or the longest side
= 9 + 16
c = √25
The sign (√) means square root
c = 5
Let c = 10 and a = 8. Find b, or the other leg.
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
= a 2
169 = a2
169 - 25 = a2
144 = a2
144 = a2
a = √144 = 12
Take the Pythagorean theorem quiz below to see how well you understand this lesson.
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