Continuation of the lateral sides AD and BC of trapezoid ABCD, intersect at point F.

Continuation of the lateral sides AD and BC of trapezoid ABCD, intersect at point F. The larger base is 25cm. if AF = 10cm, AD = 4cm. find a smaller base.

1. By the condition of the problem, the lateral side of the trapezoid is 4 cm, the base of AB is 25 cm, the length of the lateral side with continuation is 10 cm.

2. When extending the sides to the intersection, two triangles DFC and AFB were obtained, which are similar in the first sign (equality of two angles).

Let’s calculate the coefficient of similarity k = AF: DF = 10: (10 – 4) = 10: 6 = 10/6.

This means that both the larger and smaller bases of the trapezoid are in the same ratio

AB: DC = k, then DC = AB: k = 25: 10/6 = 25 * 6/10 = 15 cm.

Answer: The smaller base is 15 cm.