1. The lengths of two sides of a triangle are $5 \mathrm{~cm}$ and $2 \mathrm{~cm}$. The length of the third side in $\mathrm{cm}$ is an odd integer. What is the length of the third side?
A $1 \mathrm{~cm}$
B $3 \mathrm{~cm}$
C $5 \mathrm{~cm}$
D $7 \mathrm{~cm}$
E $9 \mathrm{~cm}$
1. C In order for the sides to be able to join up, the sum of the lengths of any two sides must be greater than the length of the remaining side (and correspondingly, the difference between the sides must be less than the length of the third side). Hence the third side is less than $5+2=7$ and more than $5-2=3$. Therefore it is $5 \mathrm{~cm}$.