Given two side, the third side must have an integral length, how to find the area of the triangle?

Question

A man has two sticks of lengths 10 inches and 16 inches. What is the area of the triangle with the longest perimeter that he could form with it such that the third side must have an integral length?

Answer 1

Let x = length of 3rd side.

The sum of the lengths of any two sides of a triangle must be greater than the 3rd.

So we have the following inequalities..

10+16 > x

x+10 > 16

x+16 > 10

Solve each of those inequalities for x and determine the intersection. Pick the largest integer value in the solution set to get the length of the 3rd side (which also gives the longest perimeter). Now that you have the lengths of the sides of the triangle, how to you find its area?

If you are not sure, do a search for "Heron's formula for area of a triangle". Or look in the index of your Geometry text for Heron's formula.