Algebra II question help?

A landscaper is designing a flower garden in the shape of a trapezoid. She wants the length of the shorter base to be 3 yards greater than the height, and the length of the longer base to be 5 yards greater than the height. For what height will the garden have an area of 170 square yards? Round to the nearest tenth of a yard.



a. 22.4 yards

b. 27.4 yards

c. 11.2 yards

d. 105.5 yards

Algebra II question help?
A=?(b1+b2)h

170=?(h+3+h+5)h

340=2h2+8h

0=2h2+8h-340

h=[ -8±√(64+2720)]/4

h=11.2 yds
Reply:b? = h+3

b? = h+5

area = (b?+b?)h/2 = 170



(b?+b?)h/2 = 170

[(h+3)+(h+5)]h/2 = 170

[2h+8]h/2 = 170

2h2/2 + 8h/2 = 170

h2 + 4h - 170 = 0



Use the quadratic formula

ah2+bh+c=0

ah2+bh+c=0

a =1

b =4

c =-170



x = [-b ± √(b2-4ac)] / (2a)

???= [-(4) ± √((4)2 - 4(1)(-170))] / 2(1)

???= [-4 ± √(696)] / 2

???= [-4 ± √(23)√(3)√(29)] / 2

???= [-4 ± 2√(2)(3)√(29)] / 2

???= -2 ± √(2)√(3)√(29)

???= -2 ± 13.191



x? = -2 + 13.191 = 11.191

x? = -2 - 13.191 = -15.191 invalid



The trapezoid will be 11.191 yards high