Question 121640
Let a and b the sides of the rectangular picture 
then 2(a+b)=34 then

 a+b=17

and using the diagonal is 13 and pitagoras then 

a^2+b^2=13^2

a^2+(17-a)^2=169
cms
a^2+289-34a+a^2=169

2a^2-34a+120=0
a^2-17a+60=0

the solution to this equation a=12  and a=5 then

the dimensions are 12 and 5 cms