SOLUTION: the perimeter of a rectangle is 74 inches. If the width is doubled and the length is halved, the new rectangle will have a perimeter is 76 inches. What are the dimensions?

Question 286489: the perimeter of a rectangle is 74 inches. If the width is doubled and the length is halved, the new rectangle will have a perimeter is 76 inches. What are the dimensions?
Answer by texttutoring(324) (Show Source): You can put this solution on YOUR website!
You have two unknowns, l=length and w=width, so you need two equations.
Recall that perimeter of a rectangle is P = 2l + 2w
Eqn 1: 74 = 2w + 2l
Eqn 2: 76 = 2(2w) + 2l/2
76 = 4w +l
Rearrange Eqn. 2, isolating for l:
l=76-4w
Insert this expression for l into Eqn 1:
74 = 2w + 2(76-4w)
74 = 2w + 152 -8w
6w = 78
w=13
The length can be found from either Eqn1 or 2:
l = 76-4w
l = 76-4(13)
l=24
So the width is 13 and the length is 24.

Let me know if you have any questions about this solution.
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