Respuesta :

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.
MrRoyal

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

The side lengths of the triangles are given as:

Lengths = 4ft, 10ft and 12ft

Pythagoras theorem states that the square of the longest length of a right-angle triangle equals the sum of the square of the other lengths.

So, we have:

[tex]12^2 = 4^2 + 10^2[/tex]

Evaluate all exponents

[tex]144 = 16 + 100[/tex]

Add 16 and 100

[tex]144 = 116[/tex]

The above equation is false; because 144 does not equal 116.

Hence, the triangle is not a right-angle triangle

Read more about Pythagoras theorem at:

https://brainly.com/question/654982

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