The height and base of the trapezoid are 5: 6: 4. Find the smaller base of the trapezoid

The height and base of the trapezoid are 5: 6: 4. Find the smaller base of the trapezoid if the area of the trapezoid is 8 cm2 and the height is less than the base.

Since the height, by condition, is less than the base, then let the length of the height be 4 * X cm, then the length of the smaller base is 5 * X cm, the length of the larger base is 6 * X cm.

We use the formula for the area of a trapezoid.

Savsd = (BC + AD) * BH / 2 = (5 * X + 6 * X) * 4 * X / 2 = 44 * X ^ 2/2 = 22 * X ^ 2.

22 * X ^ 2 = 88.

X ^ 2 = 88/22 = 4.

X = 2 cm.

Then BC = 2 * 5 = 10 cm.

Answer: The length of the smaller base is 10 cm.