The larger base of the trapezoid is 14 cm long. Find the length of the smaller base if the distance between the midpoints of the diagonals of the trapezoid is 3 cm.
Let’s draw the middle line of the HP trapezoid ABCD. The middle line of the trapezoid divides the diagonals in half, then, by condition, KM = 3 cm.
The segments НК and РМ are the middle lines of the triangles ABC and BCD, and then НК = РМ = BC / 2.
Let the length of НK = РM = X cm, then BC = 2 * X cm, and HP = (X + 3 + X) = (2 * X + 3) cm.
According to the formula of the middle line of the trapezoid: НР = (ВС + АD) / 2.
2 * X + 3 = (2 * X + 14) / 2.
4 * X + 6 = 2 * X + 14.
2 * X = 8.
X = НK = PM = 8/2 = 4 cm.
Then BC = 4 * 2 = 8 cm.
Answer: The length of the smaller base is 8 cm.
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