SOLUTION: The length of a rectange is 6in more than 3 times its width. If the width were increased by 4 and the length decreased by 10, the area of the new rectangle would equal the area of

Question 149381: The length of a rectange is 6in more than 3 times its width. If the width were increased by 4 and the length decreased by 10, the area of the new rectangle would equal the area of the orignal rectangle. Find the length and width of the original rectangle.
Found 2 solutions by jojo14344, mangopeeler07:
Answer by jojo14344(1513) (Show Source): You can put this solution on YOUR website!
Let , with following conditions:

,
So, ---->

.
Let with following conditions:

So, ---->

.
Equating the 2 Areas because of the conditions, becoming
, rearranging thereafter:
---->

Going back to the old condition for --->

In doubt? Go back
Also,

Thank you,
Jojo
Answer by mangopeeler07(462) (Show Source): You can put this solution on YOUR website!
l=3w+6------------------The length of a rectange is 6in more than 3 times its width
w=w---------------------The width
w(3w+6)=(w+4)(3w-4)-----------------If the width were increased by 4 and the length decreased by 10, the area of the new rectangle would equal the area of the orignal rectangle

Distribute
3w^2+6w=3w^2+8w-16

Subtract 3w^2 from both sides
6w=8w-16
Subtrat 8w from both sides
-2w=-16

Divide by -2
w=8

l=3w+6
w=w

Length=30
Widht=8
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