SOLUTION: The length of a rectangle is 3 times the width. When the length is decreased by 2 and the width is increased by 3. The area of this new rectangle is 42. Find the dimensions of e

Algebra ->  Linear-equations -> SOLUTION: The length of a rectangle is 3 times the width. When the length is decreased by 2 and the width is increased by 3. The area of this new rectangle is 42. Find the dimensions of e      Log On


   

Question 1053332: The length of a rectangle is 3 times the width. When the length is decreased by 2 and
the width is increased by 3. The area of this new rectangle is 42. Find the dimensions of
each rectangle.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
w and L
L=3w
Original area is wL.

Dimensions changes this way:
L-2 and w+3.
New area is (w+3)(L-2).

New area rectangle is 42.
system%28%28w%2B3%29%28L-2%29=42%2CL=3w%29
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Use algebraic or arithmetic steps to solve from that.


STEPS TO BEGIN:
%28w%2B3%29%283w-2%29-42=0
3w%5E2%2B7w-6-42=0
3w%5E2%2B7w-48=0
Look for a factorization, but immediately using formula for general solution of quadratic equation,
w=%28-7%2B-+25%29%2F6, and need the PLUS form;
w=18%2F6
highlight%28w=3%29

You can finish the work to finally answer the question.




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discriminant, 49%2B4%2A3%2A48=49%2B12%2A48=625=25%5E2