Let the length of the smaller base of the trapezoid be 3 * X cm, BC = 3 * X cm, then, by condition, the length of the larger base of the trapezoid is AD = 7 * X cm.
The area of the trapezoid is equal to the product of the half-sum of the lengths of its bases by the height.
Savsd = (3 * X + 7 * X) * BH / 2.
60 = 10 * X * 3/2.
30 * X = 120.
X = 4.
Then BC = 3 * 4 = 12 cm, AD = 7 * 4 = 28 cm.
Answer: The lengths of the bases of the trapezoid are 12 cm and 28 cm.
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