The lengths of the heights and bases of the trapezoid are proportional, respectively

The lengths of the heights and bases of the trapezoid are proportional, respectively, to the values 4, 6, 5, find the smaller base of the trapezoid if its area is 88 cm2.

Let’s denote the height of the trapezoid by h, and its bases by a and b. So h: a: b = 4: 6: 5. Hence, h = 4x, a = 6x, b = 5x. We find the area of the trapezoid by the formula: S = ((a + b) / 2) * h. Substitute the values and solve the equation: ((6x + 5x) / 2) * 4x = 88, (11x / 2) * 4x = 88, 22x = 88, x = 4. The smaller base would be b, b = 5x = 5 * 4 = 20 (cm)
Answer: 20 cm.