<p>What is the greatest possible area of a triangle with one side of length 7 and another side of length 10?</p>
<p>why is the answer 35?</p>
<p>Think about it. Try drawing a pic.
The highest height no matter what will be 10 and the farthest it will go out is 7.. just draw it and try many combos. No matter how you draw it it will always be less than 35.</p>
<p>I thought this question was weird too...is there a more algebraic/systematic way of thinking about this? I was thinking of trig but we get no angles.</p>
<p>There IS a trigonometry way :)
use the formula
1/2absinC
if you know your trig then you know sin C can be largest at most 1
so
1/2 (7)(10) - 35 which equals MAX area. Thats what the above formula solves.</p>