The length of segment AB is 40 cm Points C and D divide segment AB into segments AC, CD and DB. The length of the segment CD is 4 cm longer than the length of the segment AC, but 2 times less than the length of the segment DB. Find the length of the segment AC.
Let’s solve this problem using the equation.
Let the length of the segment CD be x centimeters, then the length of the segment DB wound is 2 * x centimeters, and the length of the segment AC is (x – 4) centimeters. We know that the length of the segment AB is 40 centimeters and it consists of the sum of the segments CD, DB and AC. Let’s make the equation:
x + 2 * x + x – 4 = 40;
x + 2 * x + x = 40 + 4;
x + 2 * x + x = 44;
x * (1 + 2 + 1) = 44;
x * 4 = 44;
x = 44: 4;
x = 11 centimeters – the length of the CD segment;
11 – 4 = 7 centimeters is the length of the AC segment.
Answer: 7 centimeters.
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