SOLUTION: Hi If the area of a rectangle is reduced by 54cm^2 then either the length is reduced by 9cm or its width is reduced by 3cm. What is the area of the original rectangle. Thanks

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Question 1196113: Hi
If the area of a rectangle is reduced by 54cm^2 then either the length is reduced by 9cm or its width is reduced by 3cm. What is the area of the original rectangle.
Thanks
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
w, L, the original dimensions width and length

system%28wL-w%28L-9%29=54%2CwL-%28w-3%29L=54%29
-
system%28wL-wL%2B9w=54%2CwL-wL%2B3L=54%29

system%289w=54%2C3L=54%29

system%28highlight%28w=6%29%2Chighlight%28L=18%29%29

Area was originally highlight%28108%2Acm%5E2%29

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


A formal algebraic solution as shown by the other tutor is valid; however, you learn a lot more about solving problems (and get much better brain exercise!) by solving this one using logical reasoning.

If a reduction in the length of 9cm produces a reduction in area of 54cm^2, then the width of the rectangle is 54/9 = 6cm.

If a reduction in the width of 3cm produces a reduction in area of 54cm^2, then the length of the rectangle is 54/3 = 18cm.

ANSWER: The area of the rectangle is 18*6 = 108cm^2.