Use the Pythagorean Theorem to determine the if a triangle with side lengths 4ft., 10 ft., and 12ft. is a right triangle?

We can use Pythagoras Theorem to prove that a triangle is a right-angle triangle if the square of the two shorter legs add up to be the square of the longest leg.

In this case, we need to prove that 4² + 10² = 12²


Pythagoras Theorem:

[tex]\boxed {\boxed { a^2 + b^2 = c^2}}[/tex]

[tex]4^2 + 10^2 = 16 + 100[/tex]

[tex]4^2 + 10^2 = 116[/tex]

[tex]4^2 + 10^2 \neq 12^2[/tex]

Therefore a triangle with side lengths 4 ft, 10ft and 12 ft is not a right angle triangle.