Question

The lengths of the sides of a triangle 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?

$\ 7$

$\ 8$

$\ 9$

$\ 10$

$\ 11$

Answer: E

Concepts:perimeter linear equation percentage

Difficulty rating: 1060

Solution:

Let $s$ be the smallest length. Then, all the side lengths are $s,s+1,s+2.$ This would make the perimeter equal to $3s+3.$ Since $s = 0.3(3s+3),$ then $s = 0.9s + 0.9 .$ This makes $0.1s = 0.9,$ so $s = 9$ which makes the longest side length $s + 2 = 11.$

Thus, the answer is E .

2010 AMC 8 Problem 13

Answer: E

Difficulty rating: 1060

Solution:

Problem 13 in Other Years