[tex]P=2L+2W[/tex]
[tex]A=WL[/tex]
Therefore, if [tex]P=34[/tex], and [tex]A=30[/tex], then let us find the factors of 30 that could give a sum of half of the perimeter which is 34. Therefore:
[tex]P=2*15+2*2[/tex]
[tex]A=15*2[/tex]
[tex]P=34[/tex]
[tex]A=30[/tex]
Therefore, the dimensions of this rectangle are 15 and 2.