A geometry problem by dhana dash
Geometry
Level
1
Two sides of scalene triangle ABC measure 3 centimeters and 5 centimeters. How many different whole centimeter lengths are possible for the third side?
4cm , 6cm ,7cm
8cm.4cm.3cm
5cm.7cm,4cm
6cm.,7cm,8cm
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1 solution
By the triangle inequality with side lengths a ≤ b ≤ c , a > c − b , and c > a + b So the third side length must be between 5 − 3 = 2 and 5 + 3 = 8 . We do not count 2 and 8 as they do not satisfy the inequality.
That leaves 3 , 4 , 5 , 6 , and 7 . But the problem says it is a scalene triangle, so lengths 3 and 5 do not count either. That leaves 4 , 6 , 7