Geometry

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Abhish

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Dec 11, 2012
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The three perpendicular distances of three sides of an equilateral triangle from a point which lies inside that triangle are 6 cm,9 cm and 12 cm respectively.The perimeter of the triangle is
1 52 √ 2 cm
2 42 √ 2 cm
3 54 √ 3 cm
4 45 √ 3 cm

I have taken a competitive examination in which this question was asked and I have given the options to choose from.Please provide the complete solution of this question ?
 
Abhish said:
The three perpendicular distances of three sides of an equilateral triangle from a point which lies inside that triangle are 6 cm,9 cm and 12 cm respectively.The perimeter of the triangle is
1 52 √ 2 cm
2 42 √ 2 cm
3 54 √ 3 cm
4 45 √ 3 cm

I have taken a competitive examination in which this question was asked and I have given the options to choose from.Please provide the complete solution of this question ?
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I am a student in India preparing for exam for mba.I am weak in concepts.I have no clue about how to solve this problem.Please help me
 
Refer to the following sketch:

triangleperimeter.jpg

The area of the entire triangle is the sum of the areas of the red, green, and blue triangles. So, we may state:

\(\displaystyle A=\dfrac{1}{2}s^2\sin(60^{\circ})=\dfrac{s}{2}(6+9+12)\)

Now, the perimeter P is:

\(\displaystyle P=3s\)

Can you find the perimeter now?
 
I've got plenty of both colors to share with everyone! :p
 
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