Carl has two pieces of wire with lengths 14cm and 18cm. How many different triangles can he make with them if the third side is to be a whole number of cm in length?
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Carl has two pieces of wire with lengths 14cm and 18cm. How many different triangles can he make with them if the third side is to be a whole number of cm in length?
The triangle inequality states that for any triangle, the sum of the lengths of any of the two sides must be greater than or equal to the length of the third side. That is, given a triangle with sides
, 
, and 
, then 
, and 
, and 
.
Thus, given that Carl has two pieces of wire with lengths 14cm and 18cm, let the two wires represent two sides of the triangle he wants to construct and let
represent the length of the third side of the triangle, then, by the triangle inequality theorem, 
.
Since,
is a length and the value is a whole number, then the possible values of 
are whole numbers from 1 to 32.
Therefore, Carl can construct 32 different triangles.