PSAT Math Question

Test Preparation
1

<p>So I really need some help with this math question. </p>

<p>The lengths of the three sides of a triangle are a, b, and c, where a is less than or equal to b and b is less than or equal to c. If a, b, and c are integers and the perimeter of the triangle is 8 what is the greatest possible value of h.
a. 1
b. 2
c. 3
d. 4
5. 5</p>

<p>So when I did this problem, I got c, which is the right answer, meaning the triangle was 1, 3, and 4. But then i thought I was being really clever by realizing that the third side of a triangle must be greater than the difference of the other two sides and less than the sum of the other two sides. (not greater/less than or EQUAL to) So I put b instead. Am I wrong in thinking this? It was written in the Princeton prep book and helped me answer another psat question correctly...</p>

<p>Thanks in advance!</p>

2

<p>sorry I meant b instead of h!</p>

3

<p>

</p>

<p>a <= b
b <= c</p>

<p>In order for b to be the greatest possible value, b must equal c. Side a cannot be 1 because that would make the two other sides 3.5 which is not an integer. If side a is 2, b and c can be 3.
a=2
b=3
c=3</p>

<p>The answer is C. Why would it not be C…?
2+3 = 5 > 3</p>