beeblebrox wrote:
EMPOWERgmatRichC wrote:
Hi gabriela2015,
That rule applies to ALL triangles, regardless of what the question is asking about. Here though, we're NOT asked for the third side, we're asked for the possible AREAS when we have those two specific side lengths.
With a side of 8 and a side of 12, the third side would fall into the falling range:
4 < third side < 20
The range of the areas will still end up being:
0 < Area <= 48
GMAT assassins aren't born, they're made,
Rich
Hi
EMPOWERgmatRichCIn a triangle: s1+s2>s3 & |s1-s2|<s3.
Which helps us in inferring that with 12 and 8 as two sides, third side will be 4<s3<20. So the sides will possibly be be 5,6,7,......19. I am only considering integers for the sake of simplicity.
That being said, will the smallest area of a triangle with above constraints not be :
(Sides = 5,12,8; Area = 0.5*5*8) & the max area be
(Sides=19,12,8 & Area = 0.5*19*12).?
So will the range of Area not be between 20 and 112?
Hence my answer will be all of the above numbers can be area of the triangle.
What's is wrong with my thought process?
chetan2u, sir can you help?
Hi beeblebrox,
When it comes to maximizing the area of a possible triangle when you know two of the sides, there are two facts that you have to remember:
1) Any side of the triangle can be the 'base' of the triangle, but the 'height' is always PERPENDICULAR to that base (re: it forms a 90 degree angle) - which means that the height might actually be outside of the triangle (and you have to be careful not to confuse any diagonal lines with the height).
2) When you know the exact lengths of two of the sides, then the largest possible area will be when those two sides form a 90 degree angle (and a right triangle).
In your two examples, neither of the measures that you use for the 'height' is actually the height.
GMAT assassins aren't born, they're made,
Rich
Contact Rich at: Rich.C@empowergmat.com