Question 340347: if the length of the diagonal of a rectangle is 50 in. and its area isa 1200 in.squared, what are its dimensions?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
As soon as I see a hypotenuse that measures some multiple of 5, I always suspect that I am dealing with a 3-4-5 right triangle. Sure enough, 30 times 40 is 1200. And there's the answer without doing any work. But I suspect you need to see the method, so here goes:
Let  represent one leg of the triangle (which is to say one dimension of the rectangle) and let  represent the other leg.
Since we know the area to be 1200 square inches, we can write:
From which we can derive:
From the Pythagorean Theorem we know:
Substituting:
^2\ =\ 50^2)
Which is to say:
Multiply both sides by 
Ewww -- that's ugly! Not to worry though.
Let  , substitute, and gather everything on the left:
Hmmm, 16 times 9 is 144 and 16 plus 9 is 25...
(u\ -\ 900)\ =\ 0)
So:
and
Toss the negative roots (we are looking for positive measures of length) and if  , then  or if  , then 
And there you have it.
John
My calculator said it, I believe it, that settles it
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