"Why does the Pythagorean theorem only work for..." solved and explained

Neil Sharp

Answered question

2022-11-24

Why does the Pythagorean theorem only work for right triangles?

Answer & Explanation

Addison Mueller

Beginner2022-11-25Added 10 answers

Pythagoras theorem: In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the there two sides.

Let's take a look at

△ A B C

, where

A B = 2 c m, B C = 3 c m a n d A C = 4 c m

We have that hypotenuse is the longest side of a triangle.
For

△ A B C

, side

A C

is a hypotenuse.
Using Pythagoras theorem, we get

{(A C)}^{2} = {(A B)}^{2} + {(B C)}^{2}

\Rightarrow

{(4)}^{2} = {(2)}^{2} + {(3)}^{2}

\Rightarrow

16 = 4 + 9

\Rightarrow

16 = 13

This is impossible.
Thus, the Pythagoras theorem does not work for this triangle.
As the hypotenuse is the longest side of a triangle and is situated opposite the right angle,
This means that the Pythagorean theorem is only accurate for right triangles.

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