SOLUTION: old rectangle with dimensions of 12x8 new rectangle has length of 15 what is the new width of the rectangle so it's dimensions are proportional to the old rectangle? Okay, so

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Question 287174: old rectangle with dimensions of 12x8
new rectangle has length of 15
what is the new width of the rectangle so it's dimensions are proportional to the old rectangle?
Okay, so I know the correct answer and how you get it but I still have a question.
Answer: 12/8=15/x, x being the width. x=10 is the correct answer but i'd like to know if there is a way of getting that answer by using the area instead. this is what i did:
12 old length/96 old area =15 new length/(A)new area
A=120
8 old width/96 old area=(w)new width/120 new area
W=10
10 is the correct answer but i wanted to know if i did it correctly, or if it is wrong and i just happen to get the same answer.
thanks!!!
Answer by richwmiller(17219) (Show Source):
You can put this solution on YOUR website!
I think your whole set of calculations was lucky.
we proportion length to length and width to width.
12/15=8/x
12/15=4/5
4/5=8/x
4x=40
x=10
How did you get the new area 120 without knowing the dimensions?
The new area is not 120 but 15*10=150
And even with the new area at 120 how did you get 10 for the width with 15 for the length?
There is a direct relationship between the length and width and the area.
So if you knew the area ahead of time it could be used to find an unknown width or length but you are just pulling numbers out of the air.
the areas are 96 and 150