<p>Reanna and Jason each drew a triangle. Both triangles have sides of length 10 and 20, and the length of the third side of each triangle is an integer. What is the greatest possible difference between the perimeters of the two triangles?</p>
<p>so the third side has to conform with the rule, which is the maximum length is shorter than the two other sides adds up with is 30 (10+20), and since the third side is an integer, so the maximum length is 29. Likewise, the minimum length has to be longer than the other two side’s subtraction, which is 10 (20-10), since it is an integer, so the minimum will be 11.</p>
<p>So the greatest possible difference should be 18.</p>
<p>This is based off of the rule that if you add up any two sides of a triangle, the sum must be equal to our greater than the length of the odd side out. The largest triangle would be a 10-20-30 - the maximum allowable perimeter. The smallest allowable triangle would be a 10-10-20. Thus, the greatest possible difference is 60-40=20. </p>
<p>Please correct me if I’m wrong - it’s been quite a few years since geometry.</p>
<p>^I’m sorry, my inequality was off. benjamin is right.</p>