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+11​=18;=21;=24;=27;=30;​56789â€‹î€ =30% of 18î€ =30% of 21î€ =30% of 24î€ =30% of 27=30% of 30​
If the shortest side is 9, then the longest side is 11.
OR
Let the three consecutive integers be side lengths x,x−1, and x−2.
x−2x−2x−20.1xx​=0.3(x+x−1+x−2)=0.3(3x−3)=0.9x−0.9=1.1=11​
The longest side is 11.
Answer: E​.
The problems on this page are the property of the MAA's American Mathematics Competitions