To find out if the three side lengths can create a triangle, the three smaller lengths must be greater than the longer length.
[tex]\bf~Option~A[/tex]
[tex]\sf~3~meters,5~meters,7~meters[/tex]
[tex]\sf3+5=8>7[/tex]
So this can create a triangle.
[tex]\bf~Option~B[/tex]
[tex]\sf1~yard,1.25~yards,1.5~yards[/tex]
[tex]\sf1+1.25=2.25>1.5[/tex]
So this can create a triangle.
[tex]\bf~Option~C[/tex]
[tex]\sf5~inches,10.5~inches,17~inches[/tex]
[tex]\boxed{\sf5+10.5=15.5<17}[/tex]
So this cannot create a triangle.
[tex]\bf~Option~D[/tex]
[tex]\sf15~millimeters,18~millimeters,30~millimeters[/tex]
[tex]\sf15+18=33>30[/tex]
So this can create a triangle.
Therefore, your answer is Option C.
