On the segment AD, points B and C are selected so that point B lies between A and C. The length of the segment AC

On the segment AD, points B and C are selected so that point B lies between A and C. The length of the segment AC is 6 cm, the length of the segment AB is 2 cm less than the length of the segment BC, the length of the segment CD is twice the length of the segment AB. Find the length of the segment AD.

Solution:

Let’s designate the segment AB as x, then BC = x + 2. Since AB + BC = AC we can make the equation:

x + (x + 2) = 6

2x +2 = 6

2x = 4

x = 2 from which it follows that AB = 2 cm, BC = 2 + 2 = 4 cm.

By the condition of the problem CD = AB * 2 = 2 * 2 = 4 cm.Now we find the total length of the segment AD = AB + BC + CD = 2 + 4 + 4 = 10 cm.

Answer: 10 cm