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# What is the smallest possible perimeter, in units, of a triangle whose side-length measures are consecutive integer values?

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What is the smallest possible perimeter, in units, of a triangle whose side-length measures are consecutive integer values?

Jul 17, 2020

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This is probably wrong but i'll give it a try.

The two smallest integers we have are 1 and 2...the sum of the sides would be smallest if the triangle is a right triangle, because it minimizes the third side. Then we can apply the pythagorean theorem to this:

1^2+2^2=c^2

1+4=c^2

c^2=5

c=$$\sqrt{5}$$.

Then the sides of this triangle are 1, 2, and $$\sqrt{5}$$. Adding them together we have 1+2+$$\sqrt{5}$$=(3+$$\sqrt{5}$$) units.

Jul 17, 2020
edited by gwenspooner85  Jul 17, 2020
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