solve this question please
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ans- A )81
Sum of perpendicular distances= Height of ∆
So the height of triangle is
6√3 + 9√3 + 12√3= 27√3
We know
![heightof \: equilateral \: triangle \: = \\ \frac{ \sqrt{3} }{2} \times a = 27 \sqrt{3 } \\ a = 54 heightof \: equilateral \: triangle \: = \\ \frac{ \sqrt{3} }{2} \times a = 27 \sqrt{3 } \\ a = 54](https://tex.z-dn.net/?f=heightof+%5C%3A+equilateral+%5C%3A+triangle+%5C%3A++%3D++%5C%5C+++%5Cfrac%7B+%5Csqrt%7B3%7D+%7D%7B2%7D++%5Ctimes+a+%3D+27+%5Csqrt%7B3+%7D++%5C%5C+a+%3D+54)
a means side of triangle
so semi perimeter of triangle is 81 cm.
![\frac{3a}{2} \\ \frac{3 \times 54}{2 } \\ 81 \frac{3a}{2} \\ \frac{3 \times 54}{2 } \\ 81](https://tex.z-dn.net/?f=+%5Cfrac%7B3a%7D%7B2%7D++%5C%5C++%5Cfrac%7B3+%5Ctimes+54%7D%7B2+%7D++%5C%5C+81)
Sum of perpendicular distances= Height of ∆
So the height of triangle is
6√3 + 9√3 + 12√3= 27√3
We know
a means side of triangle
so semi perimeter of triangle is 81 cm.
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