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![[Post New]](/templates/default/images/icon_minipost_new.gif) 14 Dec 2006 19:19:19 IST
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A 12cm long wire is bent to form a triangle with one angle 60deg,find the sides if area is maximum.(got stuck after assuming one of remaining angles and applying sine rule)
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14 Dec 2006 19:32:09 IST
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there's no need to use the concept of maxima & minima length of the wire is 12 cm so perimeter is 12 cm one of the angle's 60degrees for a given perimeter, right triangle has the highest area so other angles are 30 and 90 degrees use this data and find the sides and thus find the area of the triangle
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Talk less work more!! {To be simplistic and gain respect}
Eat less work more!!! {To "build" ur body}
Work less Do more!!! {2 make ur life big}
        
don't get scared !!!
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15 Dec 2006 21:22:50 IST
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Yes I agree upon uday_zingtudor's suggestion. Remember it as rule that the for a given perimeter the area of Right angled triangle is maximum.
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The Scientist does not study nature because it is useful; he studies it because he delights in it, & he delights in it because it is beautiful. If nature were not beautiful, it would not be worth knowing, life would not be worth living. Ofcourse I do not here speak of that beauty that strikes the senses, the beauty of qualities & appearances; not that I undervalue such beauty, far from it, but it has nothing to do with science; I mean that profounder beauty which comes from the harmoniuos order of the parts, & which a pure intelligence can grasp. |
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27 Dec 2006 12:57:41 IST
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I don't think edison is correct. For a given perimeter equilateral triangle should have the max area.
For instance, in this example the area of right angled triangle will be
1/2 * 3 * 4 = 6
However the area of equilateral triangle having each side of 4 units will be 1/2 * 4 * 2 root 3 = 6.93
This proves the fact that for a given perimeter equilateral triangle has the max area.
Can i get a feed back if my understanding is correct or wrong ?
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27 Dec 2006 21:12:54 IST
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A little correction in the above message.
The area of rt triangle with 60 deg as one of the angle will be
1/2 * 2.54 * 4.39 = 5.6 sq units. which is even lesser and much lesser than 6.93 sq units.
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27 Dec 2006 21:36:21 IST
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who says it is rule that for a given perimeter area of right triangle is maximum, forget abt it , i dunt know it is rule or not , but always remember start solving question from basics otherwise i am pretty sure u r gonna have great mix up in JEE papaer.
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life is like red red rose |
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27 Dec 2006 21:37:18 IST
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it is very simple question making the area as a function of 1 variable then differentiate to get maxima and minima condition and then value
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life is like red red rose |
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28 Dec 2006 18:51:43 IST
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i do agree with the edison it is a rule for agiven perimeter right angle triangle has the greatest area
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20 Apr 2008 12:17:49 IST
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Let me prove that:
we have a+b+c=12 and b2=a2+c2-2ac*cos B = a2+c2-ac
(a+c-12)2=b2 a2+c2+144+2ac-24a-24c=a2+c2-ac
144+3ac-24a-24c=0 48+ac-8a-8c=0, diff w.r.t. a, we get
a*dc/da + c - 8 - 8dc/da=0dc/da=(8-c)/(a-8)
Assuming B= /3
Area of triangle ABC= 1/2 * a * c * Sin B =  3/4 * ac
The area will be maximum if the product ac is maximum. differentiating and equating to 0, we get
adc+cda=0 c= -a dc/da= -a (8-c)/(a-8)
ac-8c=ac-8aa=c
Therefore the triangle is an equilateral triangle with sides 4cm each!! So the answer is not a Right angled triangle.
Cheers!
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