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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.

Respuesta :

Area of a trapezoid = ½(a + b)h, where a and b are the lengths of the parallel sides and h is its height. 

From your information 20 = ½(2z + 3 + 6z – 1)z = ½(8z + 2)z = z(4z + 1) 

Solve 20 = 4z² + z which is 0 = 4z² + z – 20 using the quadratic formula 

Answer:

20 = {(2z + 3) + (6z – 1)}/2 * z

20 = 8z+2/2 *z

20 = 4z + 1 * z

20 = 4z^2 + z

-20      -20

0 = 4z^2+z-20

Divide by 4

0 = x^2+1/4z-5

5 = x^2+1/4z

5+1/64 = x^2+1/4z + 1/64

321/64 = x^2+1/4z +1/64

321/64 = (x+1/8)^2

take square root both sides

+/- square root 321/8 = x + 1/8

subtract 1/8 both sides

+/-square root 321/8 - 1/8 = x