SOLUTION: The sum of the length and the width of a rectangular region is equal to 205 feet, whereas the corresponding positive difference is 35 feet. Find the area of the enclosed rectangula

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Question 105982: The sum of the length and the width of a rectangular region is equal to 205 feet, whereas the corresponding positive difference is 35 feet. Find the area of the enclosed rectangular region. ( Use 2-variable approaches)
Answer by alvinjohnburgos(11) About Me  (Show Source):
You can put this solution on YOUR website!
If:
L = length
W = width
The sum of the length and the width of a rectangular region is equal to 205 feet:
eqn 1:L+%2B+W+=+205
the corresponding positive difference is 35 feet:
eqn 2:L+-+W+=+35
We will use the substitution method.
Isolate W:
L+%2B+W+=+205
W+=+205+-+L
Substitute (205 - L) in eq. 2:
L+-+W+=+35
L+-+%28205+-+L%29+=+35
L+-+205+%2B+L+=+35
2L+=+240
L+=+120+feet
W+=+205+-+L+=+205+-+120+=+85+feet
Area of the rectangular region is:
A+=+LW+=+%28120%29%2885%29+=+10200
The area of the rectangular region is 10200ft^2.