+0

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

+1
92
3
+28

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

Jul 17, 2020

#1
+781
+1

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
#2
+1

assuming this is positive, your answer would be 9

This is because 2-3-4 is consecutive and follows the triangle inequality theorem

Jul 17, 2020
#3
+19
+1

3 + 4 + 5 = 12 could work. It's probably not the smallest.

Jul 17, 2020