The height AD of an equilateral triangle is 10 cm, the perimeter of triangle ADC is 70 cm.

The height AD of an equilateral triangle is 10 cm, the perimeter of triangle ADC is 70 cm. Find the perimeter of triangle ABC.

In an equilateral triangle, the lengths of all sides are equal, and the height drawn from any vertex is also the median and bisector.

1) Let’s introduce a variable.

x cm – the length of the DC side,

(2 × х) – length of the AC side.

2) Knowing the perimeter of the triangle ADC, we will compose the equation.

P = AC + AD + DC;

70 = 2 × x + 10 + x;

3 × x = 70 – 10;

3 × x = 60;

x = 60: 3;

x = 20 cm.

3) Find the side of AC

AC = 2 × x;

AC = 2 × 20;

AC = 40 cm.

4) Find the perimeter of the triangle ABC:

P = 3 × AC (equilateral triangle)

P = 3 × 40;

P = 120 cm.