How do you find one side of a right triangle

Asked by admin @ in Mathematics viewed by 287 People

A right triangle has a hypotenuse length of 12, and one side length of 9. find the missing side length. do the side lengths form a pythagorean triple?

Answered by admin @


Use the Pythagorean theorem:

a^2+b^2=c^2

c - a hypotenuse

a, b - legs

We have: a = 9 and c = 12. Substitute:

9^2+b^2=12^2

81+b^2=144               subtract 81 from both sides

b^2=63\to b=\sqrt{63}\\\\b=\sqrt{9\cdot7}\\\\b=\sqrt9\cdot\sqrt7\\\\ \boxed{b=3\sqrt{7}}

A Pythagorean triple consists of three positive integers a, b and c, such that

a^2+b^2=c^2.

b=3\sqrt{7} is not positive integer.

The sides of the triangle do not form a pythagorean triple.


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