Question

How do you know that the triangle with side lengths 6, 8, and c is a right triangle?

Answer 1

If c is the longest side, then c must be equal to 10 in order to have a right triangle. This is due to the pythagorean theorem

a^2+b^2 = c^2

6^2+8^2 = c^2

36+64 = c^2

100 = c^2

c^2 = 100

sqrt(c^2) = sqrt(100) ... apply square root to both sides

c = sqrt(100)

c = 10

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So if we know that c = 10, then the side lengths 6,8,c form a right triangle.