Question 602129
le length be x
width be y

perimeter = 2(x+y) = 34
/2
x+y =17

By Pythagoras theorem
The doagonal forms a right triangle with the sides

{{{x^2+y^2= 13^2}}}
add 2xy 

{{{x^2+2xy+y^2=169+2xy}}}


{{{(x+y)^2=169+2xy}}}
17^2=169+2xy

{{{289=169+2xy}}}

{{{289-169=2xy}}}
120=2xy
xy = 60
x= 60/y


x+y =17
60/y + y = 17
60+y^2=17y

y^2-17y+60=0
y^2-12y-5y+60=0
y(y-12)-5(y-12)=0
(y-12)(y-5)=0
y= 12cm OR 5cm

The dimensions are 12cm length & 5 cm width