The length of the broken line ABCD is equal to the perimeter of the triangle ABC The sum of the segments AC

The length of the broken line ABCD is equal to the perimeter of the triangle ABC The sum of the segments AC and CD is 56 cm, and the sum of AB and CD is 62 cm. BC is less than AC by Xcm. Find the length of the polyline ABCD. Simplify the expression and calculate with X = 8.

1. The length of the polyline ABCD is equal to the perimeter of the triangle ABC, we write it down:
ABCD = PABC;
2. Let’s write the expressions:
ABCD = AB + BC + CD;
PABC = AB + BC + AC;
ABCD = PABC;
AB + BC + CD = AB + BC + AC;
CD = AC;
AC + CD = 56 cm;
AC = CD = 56/2 = 28 (cm);
AB + CD = 62 cm;
AB = 62 – СD = 62 – 28 = 34 (cm);
BC = AC – x = 28 – x;
3. Let us express the length of the polyline:
ABCD = 34 + 28 – x + 28 = 90 – x;
4. Calculate the length of the polyline:
ABCD = 90 – x = 90 – 8 = 82 (cm);
Answer: the length of the broken line is 82 centimeters.