Question

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 ?​

Answer 1

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 ?​

Answer 2

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.