How to find the length of the larger and smaller base if it is known that the length of the midline is 9 cm.A (a-b = 4)

Let a trapezoid ABCD be given, which has a larger base AD = a cm, a smaller base BC = b cm.It is known from the problem statement that the length of the middle line is 9 cm, which means (a + b): 2 = 9 (cm) or a + b = 18 (cm), since the length of the midline of the trapezoid is half the sum of the bases. Knowing that the base difference a – b = 4 (cm), we obtain a system of equations with two unknowns:
a + b = 18 and a – b = 4;
a = 11 (cm) – the length of the larger base of the trapezoid AD;
b = 11 – 4 = 7 (cm)
Answer: the lengths of the larger and smaller bases of the trapezoid are 11 and 7 cm.