In the quadrilateral ABCD side AB = x cm. Express the other sides of this quadrilateral: BC is 3 cm less than ABCD

In the quadrilateral ABCD side AB = x cm. Express the other sides of this quadrilateral: BC is 3 cm less than ABCD is 1.125 times more than ABAD and 3 times more than CD. Make an equation knowing that the perimeter of ABCD is 10.2 cm. Solve the resulting equation. Find the length of AB.

Let us express the length of the side BC through AB, knowing that BC is 3 cm less than x:
BC + 3 = x;
BC = x – 3 (cm).
Let us express the length of the side CD in terms of AB, knowing that CD is 1.125 times greater than x:
CD: 1.125 = x;
CD = x * 1.125 (cm).
Express the length of the AD side in terms of CD, knowing that AD is 3 times longer than CD:
AD = 1.125x * 3;
AD = 3.375x.
Let’s compose the equation for the perimeter:
AB + BC + CD + AD = 10.2;
x + x – 3 + 1.125x + 3.375x = 10.2;
6.5x – 3 = 10.2;
6.5x = 10.2 + 3;
6.5x = 13.2;
x = 13.2: 6.5;
x = 2.03 (cm).
AB = x = 2.03 cm.
ANSWER: side AB is 2.03 cm.