<p>If the length of AB is 5 and the length of BC is 6 which of the following could be the length of AC?
A) 10 B) 12 C) 13 D) 15 E) 16
the answers say A but how?</p>
<p>It’s a triangle question. Sides of 5 and 6 mean that the third side must be less than 11 (2 sides of a triangle added up must be greater than the length of the third side). </p>
<p>A. 10 is the only option that fulfills this requirement.</p>
<p>Thanks a lot. That was really tricky to me.</p>
<p>In general use the Triangle Rule which says “the length of the third side of a triangle is strictly between the difference and sum of the lengths of the other two sides.”</p>
<p>In this case 6-5=1 and 6+5=11. So 1<AC<11.</p>
<p>Note: In this example you didn’t need the difference, but it’s good to know the whole rule.</p>
<p>To prove it, draw segment BC such that BC = 6. Draw a circle of radius 5 centered at B. A can be any point on the circle so that ABC is a triangle. Here it is evident that 1 < AC < 11.</p>