Multiplying and dividing fractions

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Cwkerr

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A garden shares a wall with a barn. The area of the barn is 225 square feet and the area of the garden is 75 square feet. What is the greatest length of the shared wall?
 
Firstly is this the full question? What have you tried? where are you stuck?
 
At first I thought I should try to find the greatest common factor but that is 75 and doesn’t seem correct. I am stumped on this one.
 
It's a somewhat interesting question to ponder, but I don't think it involves much in the way of fractions.

To clarify, I would guess the intent is that the barn and garden are both rectangular, and that the shared wall is an entire side of the barn and an entire side of the garden. And I suppose "the greatest length" means "the greatest possible length, considering all possible barns and gardens fitting this description", since there is only one shared wall, not several to be compared.

Then, my first question would be, how wide does a garden have to be, to be still considered a garden?
 
Cwkerr said:
At first I thought I should try to find the greatest common factor but that is 75 and doesn’t seem correct. I am stumped on this one.
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If your context suggests something about GCF, then perhaps they are expecting you to assume that all dimensions of the barn and garden are whole numbers of feet. (If you know anything about construction or gardening, you would never make that assumption ...)

If that silly assumption is true, then you may be "correct", since the GCF of 75 and 225 is 75: the largest possible side of the garden would be 75 feet, which is a factor of 225, so the barn would be 75x3 feet, while the garden would be 75x1 foot. The garden couldn't be any thinner than that under the assumption.

I guess a silly question has a silly answer. Or maybe there's yet another assumption you're expected to make. I think you're smarter than that, though.

The correct answer, as I read it, is that the "garden" is 8 inches of dirt along the side of the "barn", which is 112 feet long and two rows of studs wide. It's really a billboard.
 
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