SOLUTION: The problem says:
Nicole's new house has a small deck that measures 6 feet by 12 feet. She would like to build a larger deck. By what amount must each dimension be increased to
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Question 252051: The problem says:
Nicole's new house has a small deck that measures 6 feet by 12 feet. She would like to build a larger deck. By what amount must each dimension be increased to triple the area of the original deck?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The problem does not give you sufficient information to derive a unique solution. Never mind the given dimensions, let's discuss the area of any rectangle. The area is simply the length times the width, thus:
but if we want to triple then area, then:
That tells me that I could make the length 3 times longer and leave the width the way it is, or I could make the width three times greater and leave the length alone -- or any of an infinite number of possibilities in between. One way to interpret your problem is to assume that the increase must keep the original proportions of the deck intact, meaning that you would have to multiply each of the dimensions times some factor 
so that
(kw))
Which would mean that
And the new dimensions would be 
wide by 
long and the amount of increase to each dimension would be 
and 
.
On the other hand, the question might mean to ask: "What is the single fixed amount that should be added to each of the dimensions such that the new area is three times greater than the original?"
In this case, let 
represent the amount of increase to each side. Then the new area would be:
(x\,+\,12)\ =\ 3\,\cdot\,72)
(x\,-\,6)\ =\ 0)
Discard the negative root and 
John
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