Question 87085
Use the formula for the Area:
Area = (length)(width)
Area = 60 [plug-in the values that are given]
Sovling for either L or W will be too confusing, so...
.
Use the formula for Perimeter:
P=2(length + width)
P=34 [plug-in the values that are given]
34=2(length + width)
34/2=2(length + width)/2 [solve for either the Width or the Length]
17=length + width
17-width=length+width-width
17-width=length
17-W=L
.
Area=(L)(W)
60=(17-W)(W) [plug-in the values and simplify]
60=17W-w^2 [set the equation equal to zero by adding/subtraction from both sides
60-17W+w^2=-17W+17W-W^2+W^2
60-17W+W^2=0 [re-arrange the terms]
w^2-17W+60=0 [factor]
(W-12)(W-5)=0 [set each factor equal to zero and solve for the W-term]
W-12=0
W=12
or 
W-5=0
W=5
.
Since the width is the smallest of the 5 and 12, let 5=width and let 12 = length.

Check by plugging everything back into both equations.
A=LW
60=(12)(5)
60=60 [checks out]
and
P=2(length + width)
34=2(12+5)
34=2(17)
34=34 [also checks out]