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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

Public Comments

1. A=½(b1+b2)h 170=½(h+3+h+5)h 340=2h²+8h 0=2h²+8h-340 h=[ -8±√(64+2720)]/4 h=11.2 yds
2. b₁ = h+3 b₂ = h+5 area = (b₁+b₂)h/2 = 170 (b₁+b₂)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