Take a point \(O\) from which three line segments \(OA, OB, OC\), lying on the same plane, emanate such that their respective lengths are \(a, b, c\) and the angle between any two of them is 120 degrees. Use Cosine rule and the mentioned equations to find \(AB, BC, CA\) which will have values 3,4 and 5 units. Now this triangle \(ABC\) is right angled( by the converse of Pythagoras' Theorem), so it's area will be 6 sq. units. Also, the area of the three triangles \(AOB, BOC, COA\) can be found out by the sine rule (individually), and now equate it with the earlier found area. The answer comes out to be \(8 \sqrt{3}\). [ the calculations are to be done by you].
–
Shourya Pandey
·
3 years, 8 months ago

@Shourya Pandey
–
Well, your idea is interesting, but are you sure about the value of ab + bc +ac? shouldn' it be 8*sqrt(3)? Could you chek it again, plz??
–
Sinuhé Ancelmo
·
3 years, 8 months ago

## Comments

Sort by:

TopNewestTake a point \(O\) from which three line segments \(OA, OB, OC\), lying on the same plane, emanate such that their respective lengths are \(a, b, c\) and the angle between any two of them is 120 degrees. Use Cosine rule and the mentioned equations to find \(AB, BC, CA\) which will have values 3,4 and 5 units. Now this triangle \(ABC\) is right angled( by the converse of Pythagoras' Theorem), so it's area will be 6 sq. units. Also, the area of the three triangles \(AOB, BOC, COA\) can be found out by the sine rule (individually), and now equate it with the earlier found area. The answer comes out to be \(8 \sqrt{3}\). [ the calculations are to be done by you]. – Shourya Pandey · 3 years, 8 months ago

Log in to reply

– One Top · 3 years, 8 months ago

Is it possible to solve this algebraically?Log in to reply

– Sinuhé Ancelmo · 3 years, 8 months ago

Well, your idea is interesting, but are you sure about the value of ab + bc +ac? shouldn' it be 8*sqrt(3)? Could you chek it again, plz??Log in to reply

– Sinuhé Ancelmo · 3 years, 8 months ago

Could you show any algebraic, only algebraic solution, friend?Log in to reply

– Shourya Pandey · 3 years, 8 months ago

Edited.Log in to reply

– Sinuhé Ancelmo · 3 years, 8 months ago

You can realize that - 8 * sqrt (3) is also a valid answer for ab + bc + ac, right?Log in to reply

– Sinuhé Ancelmo · 3 years, 8 months ago

Thanks! Already read your edition, friend!Log in to reply

what will be the algebric solution Help me – Anit Singh · 2 years ago

Log in to reply

The solution could be algebraical or geometrical, Thanks in advance for help! – Sinuhé Ancelmo · 3 years, 8 months ago

Log in to reply