SOLUTION: A rectangular piece of sheet metal is 3 in. longer than it is wide. If the length and width are both increased by 2 in. the area increases by 34 in squared. What are the original

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Question 263662: A rectangular piece of sheet metal is 3 in. longer than it is wide. If the length and width are both increased by 2 in. the area increases by 34 in squared. What are the original dimensions of the sheet metal?
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
Given what we know about rectangles...
A = area = l * w
.
We are told: l = w+3
.
If we set l+2 and w+2 (that is we increase both by 2), then area = A + 34 sq in.
.
We need to define everything in terms of one term.
l = w+3
So
l+2 = w+5
.
That means:
Original Area = w(w+3)
.
And the new area is: (w+2)(w+5).
.
Combining the facts we have at hand:
w(w+3) + 34 = (w+2)(w+5)
w^2 + 3w + 34 = w^2 + 7w + 10
Subtracting w^2 from both sides
3w + 34 = 7w + 10
Subtracting 10 from both sides
3w + 24 = 7w
Subtracting 3w from both sides
24 = 4w
4w = 24
w = 6
.
Recall 'w' is the original width. The length 'l' = w+3, so it is 9.
.
We need to check our work by comparing the areas to see if they are different by 34.
A = 6*9 = 54
.
The new dimensions are: 8 & 11
New Area = 8*11 = 88
.
54+34 = 88. OK
.
Answer: The original dimensions of the sheet of metal are 6 by 9 inches.