precalc question?

Question: ive been trying forever to figure out this problem and id really appreciate some help. "A rectangle inscribed in an equilateral triangle with a perimeter of 30 cm. a) express area 'A' of the rectangle as a function of the height 'H' cm of the rectangle. b) Find the dimensions of the rectangle with the largest area."

Answer: Since thre perimeter is given, then 30 = 2H + 2L L = 15 - H A = LH, so A = (15 - H)H or A = 15H - H^2 Since the area function is quadratic in nature, then the maximum is at the vertex of the parabola. V(h,k) where h = -b/2a, and k = (4ac-b^2)/4a Since we are only interested in the dimensions of the rectangle, getting h (which in the area function represents H) we have h = -15/2(1) h = 7.5, which should also be the height of your rectangle. L = 15 - H L = 15 - 7.5 L = 7.5 So the rectangle has to have dimensions of 7.5 by 7.5. (Note that this means the rectangle must be a square) Hope that helps!!!

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