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ARITHMETIC PAPER QUESTION :-
LENTHS OF THE PERPENDICULAR FROM A POINT IN THE INTERIOR OF
AN EQUILATERAL TRIANGLE ON ITS SIDES ARE 3cm,4cm and
5cm.AREA OF THE TRIANGLE IS (A) 48√3 ; (B) 54√3 ; (C)
72√3 ; (D) 80√3.
PLEASE SOLVE SUBJECTIVELY AND SHOW PROCESS ALSO.
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The answer is (A) 48√3.
Let ABC be the Equilateral triangle & O be a point in the
interior of the triangle.
OD,OE & OF BE the respective altitudes drawn on side BC,CA
& AB.
jOIN OA,OB&OC.
Then we have three triangles inside the triangle ABC;Namely
triangle OAB,triangle OBC & triangle OAC.
Now,Area of Equilateral triangle ABC = Sum of the area of
the three triangles OAB,OBC & OAC.
AREA of triangle OBC = 1/2(BC*OE)= 1/2(x*4)
AREA of triangle OAC = 1/2(AC*OF)= 1/2(x*5)
AREA of triangle OAB = 1/2(AB*OD)= 1/2(x*3)
Where,AB = BC = CA = x
BUT,
√3/4(x2)=1/2(x*4)+1/2(x*5)+1/2(x*3)
SOLVE for x.
AND find the AREA by using the formula:
AREA of an Equilateral Triangle = √3/4 (side)2 = √3/4(x2).
| Is This Answer Correct ? | 6 Yes | 3 No |
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