# The height of the trapezoid is three times the height of one of the bases

The height of the trapezoid is three times the height of one of the bases, but half the size of the other base. Find these bases if the area is 168 cm2.

Let the length of the height of the trapezoid be equal to BH = 3 * X cm, then the smaller base is equal to BC = 3 * X / 3 = X cm, and the length of the larger base is equal to AD = 3 * X * 2 = 6 * X cm.

The area of the trapezoid is equal to: Savsd = (BC + AD) * BH / 2 = (X + 6 * X) * 3 * X / 2.

Savsd = 21 * X ^ 2/2 = 168.

X ^ 2 = 168 * 2/21 = 16.

X = BC = 4 cm.

Then AD = 6 * 4 = 24 cm.

Answer: The length of the smaller base of the trapezoid is 4 cm, the larger one is 24 cm.

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