Question

Two of the sides of a triangle are $18$ and $25.$ The length of the third side is also a positive integer. How many different possible values are there for the third side length? Ps: (Geometry Problem) Have fun!

Answer 1

A set of all positive integers between 7 and 43.

Explanation:

If a triangle is given with the sides a, b, c, triangle is possible when,

a + b > c

a + c > b

b + c > a

Following the same rule in a triangle having side lengths 18, 25 and l unit.

18 + 25 > l ⇒ l < 43

18 + l > 25 ⇒ l > 7

25 + l > 18 ⇒ l > -7

Therefore, length of the third side of the triangle will be,

7 < l < 43 (A set of positive integers between 7 and 43)