The maximum area of the triangle whose sides a,b and c satisfy 0≤a≤1 , 1≤b≤2 , 2≤c≤3 is : A) 1 B) 2 C) 1.5 D) 0.5 ?


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Question Number 31409 by rahul 19 last updated on 08/Mar/18

$T h e m a x i m u m a r e a o f t h e t r i a n g l e$ $w h o s e s i d e s a, b a n d c s a t i s f y$ $0 ⩽ a ⩽ 1, 1 ⩽ b ⩽ 2, 2 ⩽ c ⩽ 3 i s :$ $A) 1$ $B) 2$ $C) 1.5$ $D) 0.5 ?$
	Answered by MJS last updated on 08/Mar/18

	$I think because of a + b > c, a + c > b$ $and b + c > a and A r e a = \frac{s \times h_{s}}{2} with$ $s = a \lor b \lor c the largest possible$ $triangle in this case is the one$ $with \max s and \max h_{s} and it$ $seems to me {it}^{'} s the rectangular$ $one with b = 2; a = h_{b} = 1; c = \sqrt{5}$ $and \frac{b \times h_{b}}{2} = 1, so {it}^{'} s answer 1$
	Commented by rahul 19 last updated on 09/Mar/18

	$s i r w h y u c h o o s e r i g h t a n g l e d t r i a n g l e .$ $w h y n o t a n a c u t e / o b t u s e a n g l e d t r i a n g l e$
	Commented by rahul 19 last updated on 09/Mar/18

	$y o u r a n s w e r i s c o r r e c t b u t p l z g i v e r e a s o n .$
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