SOLUTION: the perimeter of a rectangle is 110 ft. and the area is 684 sq. ft. What is the length of the longer side

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Question 570937: the perimeter of a rectangle is 110 ft. and the area is 684 sq. ft. What is the length of the longer side
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
length(l) width(w) perimeter(p) area(a)
given:
2l%2B2w=p = 2%28l%2Bw%29=p = l%2Bw=p%2F2
lw=a
p=110
a=684
.
so:
l%2Bw=p%2F2
l%2Bw=110%2F2
l%2Bw=55
l=55-w
.
lw=a
%2855-w%29w=684
w%5E2-55w=-684
w%5E2-55w%2B684=0 (684=2*2*3*3*19) , (-36*-19=684) , (-36+-19=-55)
%28w-36%29%28w-19%29=0
w=36 or 19
.
l=55-w
l=55-36
l=19 or 36
.
36 is the length of the longer side