The perpendicular distances from a point inside the equilateral triangle to the sides of the triangle are 7 cm, 10 cm and 13 cm. Find the perimeter of the triangle is.
Answer & explanation
Correct answer: option 2
ΔABC is equilateral with sides "a".
P1 = 7 cm
P2 = 10 cm
P3 = 13 cm
In this condition the formula to find the length of sides is:
a = \(\frac{2}{\sqrt{3}}(P_1+P_2+P_3)\)
a = \(\frac{2}{\sqrt{3}}(7+10+13)\)
a = \(\frac{2}{\sqrt{3}}×30= 2 × 10\sqrt{3}\) = 20\sqrt{3}\)
Perimeter = 3a = 3 × \(20\sqrt{3}= 60 \sqrt{3}\)