A trapezoid has an area of 20 cm2 and a height z cm. The lengths of the parallel sides are (2z + 3) cm and (6z – 1) cm. Find the height, z, of the trapezoid. In your final answer, include all of the formulas and calculations necessary.
Accepted Solution
A:
Answer: 2.11cmStep-by-step explanation:Given the following :The lengths of the parallel sides are (2z + 3) cm and (6z – 1) cmThe area of trapezoid is calculated using the formula:1/2(a + b) × hWhere ;a = Length of side 1 b = length of side 2h = height Take a = (2z + 3) and b = (6z – 1), h = zTherefore ;1/2 (2z + 3 + 6z - 1) × zOpening the bracket(z + 1.5 + 3z - 0.5) × z(4z + 1 ) × z = 20cm^24z^2 + z = 20cm^2Using Quadratic formula:4z^2 + z - 20 = 0a = 4, b = 1, c = - 20(-b±√b^2 -4ac) / 2aZ = 2.11 or - 2.364z cannot be negative, therefore, Z = 2.11 cm