SOLUTION: Find the dimensions of a rug whose perimeter is 42 ft and area is 108 sq.ft.

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Question 806024: Find the dimensions of a rug whose perimeter is 42 ft and area is 108 sq.ft.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
given:
P=42ft and
A=108ft%5E2
we know that P=2L%2B2W and A=LW where L=length and W=width
so, we have
42ft=2L%2B2W.........eq.1
108ft%5E2=LW..........eq.2
________________________________solve this system
42ft=2L%2B2W.........eq.1........solve for L
42ft-2W=2L+
42ft%2F2-2W%2F2=L+
21ft-W=L+.....eq.1a.......substitute in eq.2

108ft%5E2=%2821ft-W%29W..........eq.2
108ft%5E2=21Wft-W%5E2
W%5E2-21Wft%2B108ft%5E2=0......factor

W%5E2-12Wft-9Wft%2B108ft%5E2=0........group
%28W%5E2-12Wft%29-%289Wft-108ft%5E2%29=0
W%28W-12ft%29-9ft%28W-12ft%29=0
%28W-12ft%29%28W-9ft%29+=+0
solutions:
if
%28W-12ft%29++=+0 ==>W=12ft
if +%28W-9ft%29+=+0==>+W=9ft
now find the length

21ft-W=L+.....eq.1a ==>W=12ft

21ft-12ft=L+

9ft=L+
or
21ft-W=L+.....eq.1a ==>W=9ft

21ft-9ft=L+

12ft=L+
so, the dimensions of a rug are: L=12ft++ and W=9ft or vs