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Homework help,algebra 2?

A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter base to be 3 yards greater than the height and the longer base to be 7 yards greater than the height. She wants the area to be 210 square yards. The situation is modeled by the equation . Use the Quadratic Formula to find the height that will give the desired area. Round to the nearest hundredth of a yard. a. 12.21 yards c. 14.71 yards b. 24.41 yards d. 430 yards

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1. The equation of the area of a trapezoid is: A = (1/2)(b1 + b2)(h) If we're told that one base is 3 yards greater than the height: b1 = h + 3 And the other base is 7 yards greater tha the height: b2 = h + 7 And the area she wants is 210 yards². Plug them in and solve for h: A = (1/2)(b1 + b2)(h) 210 = (1/2)((h + 3) + (h + 7))(h) 210 = (1/2)(2h + 10)h 210 = (h + 5)h 210 = h² + 5h 0 = h² + 5h - 210 Now use quadratic equation: h = ( -b ± √(b² - 4ac)) / (2a) h = ( -5 ± √(5² - 4(1)(-210)) / 2(1) h = ( -5 ± √(25 + 840)) / 2 h = ( -5 ± √(865)) / 2 Since they want things rounded to the nearest hundreth of a yard, I'll convert the square root to three decimal places to complete the math, then round it to two: h = ( -5 ± 29.411) / 2 h = (-5 - 29.411) / 2 and h = (-5 + 29.411) / 2 h = 34.411 / 2 and h = 24.411 / 2 h = -17.2055 and h = 12.2055 Since we can't have a negative distance, we'll throw that out, leaving 12.21 yards is your height.
2. A = area h = height L = length of longer base l = length of shorter base A = [(L + l)/2]h l = h + 3 L = h + 7 A = [(h + 7 + h + 3)/2]h A = [(2h + 10)/2]h A = [h + 5]h A = h^2 + 5h A = 210 h^2 + 5h = 210 h^2 + 5h - 210 = 0 Use the Quadratic Formula: x = [-b +/- sqrt(b^2 - 4ac)]/2a Let x = h a = 1 b = 5 c = -210 h = [-5 +/- sqrt(5^2 - 4(1)(-210))]/2(1) h = [-5 +/- sqrt(25 + 840)]/2 h = [-5 +/- sqrt(865)]/2 h = [-5 +/- 29.41]/2 h = 24.41/2 or -34.41/2 ELIMINATE (-) answer as not possible. h = 12.21 yards Choice a