One base of the trapezoid is 4cm larger than the other and the middle line is 8cm find the base of the trapezoid.

We denote by x the length of the smaller base of this trapezoid.

According to the condition of the problem, one base of this trapezoid is 4 cm larger than the other, therefore, the length of the larger base of this trapezoid is x + 4.

It is also known that the length of the midline of this trapezoid is 8 cm

Since in any trapezoid the length of the middle line of the trapezoid is equal to the half-sum of the lengths of the bases of this trapezoid, we can compose the following equation:

(x + x + 4) / 2 = 8.

Solving this equation, we get:

2x + 4 = 8 * 2;

2x + 4 = 16;

2x = 16 – 4;

2x = 12;

x = 12/2;

x = 6 cm.

We find the length of the larger base:

x + 4 = 6 + 4 = 10 cm.

Answer: the lengths of the base of this trapezoid are 6 cm and 10 cm.