If a triangle $PQR$ is constructed such that All sides are integers ; and , $PQ= 37 , QR= M$ , and $M <37$ , then the possible values of $PR$ :

Question

If a triangle $PQR$ is constructed such that All sides are integers ; and , $PQ= 37 , QR= M$ , and $M <37$ , then the possible values of $PR$ :

A) $2M-2$

B)$2M-1$

C)$2M$

D)$2M+1$

I tried to apply triangle inequality

$37-M <PR <M+37$ $1 <PR <2M+1$ since Max (m)=$36$

But i can't reject except $D$ ; what should I do?

Answer 1

Your question is confused, but from $PR<M+37$ you can't conclude $PR<2M+1$, you can only say $PR<max(M)+37$