A = (1/2) b * h h = b - 5 42 = (1/2) * b * (b - 5) 42 = (1/2) * b^2 - 5b multiply both sides by 2 to clear the fraction (1/2) 2(42) = 2(1/2) *b^2 - 5b 84 = b^2 -5b Since this is a quadratic equation, subtract 84 from both sides so that it is set = to zero. b^2 - 5b - 84 = 0 Now factor. (b - 12)(b + 5) = 0 b - 12 = 0; b = 12 b + 5 = 0; b = -5 You can't have a negative length so the answer is 12m To check the answer: A = (1/2) * 12* 7 A = 42 m^2
