SOLUTION: The area of a rectangle is 18 square meters. When the length is increased by 2 meters and the width by 3 meters the area becames 48 square meters. Find the dimensions of the smalle

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Question 84840This question is from textbook Elementry and Entermeditate Algebra
: The area of a rectangle is 18 square meters. When the length is increased by 2 meters and the width by 3 meters the area becames 48 square meters. Find the dimensions of the smaller triangle.
Just by looking at this problem I can tell the answer is 6 meters and 3 meters. But I can not figure out how to set up the forula.
I tried (m+2)(m+3)=48
I then used FOIL then used the quadratic formula but it didn't work.
Can anybody help
Thanks. This question is from textbook Elementry and Entermeditate Algebra

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
w = width
l = length
w%2Al+=+18
divide both sides by l
w+=+18%2Fl
%28w+%2B+3%29%28l+%2B+2%29+=+48%29
w%2Al+%2B+3l+%2B+2w+%2B+6+=+48
18+%2B+3l+%2B+2%2A%2818%2Fl%29+%2B+6+=+48
3l+%2B+36%2Fl+=+24
multiply both sides by l
3l%5E2+%2B+36+=+24l
3l%5E2+-+24l+%2B+36+=+0
divide both sides by 3
l%5E2+-+8l+%2B+12+=+0
%28l+-+2%29%28l+-+6%29+=+0
Two values of l make this equation true, l = 2 and l = 6
Going back to w+=+18%2Fl, if
l = 2
w = 9
Then going back to %28w+%2B+3%29%28l+%2B+2%29+=+48%29
%289+%2B+3%29%282+%2B+2%29+=+48%29 This is true, so those values work
-----------------------
w+=+18%2Fl
If l = 6, then
w = 3
%28w+%2B+3%29%28l+%2B+2%29+=+48%29
%283+%2B+3%29%286+%2B+2%29+=+48 This is true also, so both
l = 2, w = 9
and
l = 6
w = 3
are both solutions. Take your pick