the ?: what is the maximum possible area of a triangle with a length of 7 units and another side length of 8?
I know the answer is alluding the to the fact that you should take a right triangle .5(7*8) for max area....but should you take the possibility of a 3rd side into consideration because it can be from 1 to 14? (3rd side >7-8 & <7+8)
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- gmatxyz
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- RonPurewal
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Re: geometry strategy guide problem set p68 #4
the length of the third side won't help you here.
the range is even bigger than you're indicating here, by the way; the third side can be any number greater than 0 and less than 15.
however, of all those triangles, the right triangle is the one with the greatest area.
if you don't see why this is so, try drawing the triangles. (pick one of the sides-- say, the '8'-- and keep it horizontal, to facilitate a comparison of the areas.)
the range is even bigger than you're indicating here, by the way; the third side can be any number greater than 0 and less than 15.
however, of all those triangles, the right triangle is the one with the greatest area.
if you don't see why this is so, try drawing the triangles. (pick one of the sides-- say, the '8'-- and keep it horizontal, to facilitate a comparison of the areas.)
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