Math, asked by ItzzHarsh, 6 months ago

From a point in the interior of an equilateral triangle the perpendicular distances of the sides √3 cm, 2√3 cm and 5√3. What is the perimeter (in cm) of the triangle ?​

Answers

Answered by Anonymous
1

Answer:

\huge\underline\bold {Answer:}

Ler each side of the triangle be a cm.

Area of triangle ABC = Area of triangle AOB + Area of triangle AOC + Area of triangle BOC

 =  >  \frac{ \sqrt{3} }{4} a {}^{2}  =  \frac{1}{2}  \times a \times  \sqrt{3}  +  \frac{1}{2}  \times a \times 2 \sqrt{3}  +  \frac{1}{2}  \times a \times 5 \sqrt{3}

 =  >  \frac{ \sqrt{3} }{4} a {}^{2}  =  \frac{1}{2} a( \sqrt{3}  + 2 \sqrt{3}  + 5 \sqrt{3} )

 =  >  \frac{ \sqrt{3} }{4}a {}^{2}   =  \frac{1}{2}  \times a \times 8 \sqrt{3}  \\  =  >  \frac{ \sqrt{3} }{4} a =  \frac{1}{2}  \times 8 \sqrt{3}

 =  > a =   \frac{8 \sqrt{3} }{2}  \times  \frac{4}{ \sqrt{3} }  \\  =  > a = 16

Therefore, perimeter of the triangle

= 16 × 3 = 48 cm.

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