In an equilateral triangle ABC, from the middle D of side AB, a perpendicular DM is drawn to the side AC, with M

In an equilateral triangle ABC, from the middle D of side AB, a perpendicular DM is drawn to the side AC, with M € AC. Find the perimeter of the triangle ABC if AM = 7cm.

Given:
Equilateral triangle ABC,
D middle of side AB,
DM perpendicular to the AC side,
M € AC,
AM = 7 cm.
Find the perimeter of triangle ABC -?
Solution:
1) Consider an equilateral triangle ABC.
Angle A = angle B = angle C = 60 degrees;
2) consider a right-angled triangle ADM. Angle D = 180 – (90 + 60) = 30 degrees.
In a right-angled triangle, the leg opposite an angle of 30 degrees is equal to half the hypotenuse.
AD = 2 * AM;
AD = 2 * 7;
AD = 14 centimeters;
3) Since D is the middle of the AB side, then AB = 14 * 2 = 28 centimeters.
Then Ravs = 28 * 3 = 84 centimeters.
Answer: 84 centimeters.