Question

If 5 and 12 are the two smallest values in a Pythagorean triple, what is the largest value, c, in the triple?

Answer 1

Answer: 13

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Work Shown:

a^2 + b^2 = c^2

c = sqrt( a^2 + b^2 )

c = sqrt( 5^2 + 12^2 )

c = sqrt( 25 + 144 )

c = sqrt( 169 )

c = 13

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Extra info (optional section)

The perimeter is 5+12+13 = 30 units and the area is base*height/2 = 5*12/2 = 60/2 = 30 square units. In this triangle type, the area and perimeter are the same value (different units though of course). This concept and particular triangle is discussed in the video titled "Superhero triangles" from Numberphile (timestamp around 1:23 of the video).

Answer 2

13 would be the largest value in the triple.