In trapezoid ABCD, points K and F are the midpoints of BC and AD, respectively; KF = 2 m, MN = 4 m.

In trapezoid ABCD, points K and F are the midpoints of BC and AD, respectively; KF = 2 m, MN = 4 m. Find the lengths of the bases of the trapezoid and their sum.

Let us denote the upper base through – x, and the lower base through – y, then the following system can be written from the trapezoid property:

(x – y) \ 2 = 2 and (x + y) \ 2 = 4. Simplify and perform the actions:

x – y = 4 and x + y = 8.

We express x through y in the first equality and substitute it into the second equation of the system.

x = 4 + y, 4 + y + y = 8, we find y,

y = 2, and then x = 4 + 2 = 6, check the found roots: 6 + 2 = 8.

Answer. The length of the bases is 6 m and 2 m.The sum of the bases is 8 m.