Problem:
The lengths of the sides of a triangle measured in inches are three consecutive integers. The length of the shortest side is 30% of the perimeter. What is the length of the longest side?
Answer Choices:
A. 7
B. 8
C. 9
D. 10
E. 11
Solution:
One strategy is to try the choices:
5+6+76+7+87+8+98+9+109+10+11β=18;=21;=24;=27;=30;β56789βξ =30% of 18ξ =30% of 21ξ =30% of 24ξ =30% of 27=30% of 30β
If the shortest side is 9, then the longest side is 11.
OR
Let the three consecutive integers be side lengths x,xβ1, and xβ2.
xβ2xβ2xβ20.1xxβ=0.3(x+xβ1+xβ2)=0.3(3xβ3)=0.9xβ0.9=1.1=11β
The longest side is 11.
Answer: Eβ.
The problems on this page are the property of the MAA's American Mathematics Competitions