150 feet of fencing 10 foot opening for entrance what dimensions of garden for maximum area? find quadractic equation for area of garden, dimesions of garden so area is maximized, max area of garden?

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Lisa -A big part of advanced algebra is being able to picture in your mind (or a sketch on paper) what the problem is asking.For this problem, you have a rectangular garden that has a perimeter of 150 feet.  You might want to draw what I'm describing on paper:One side has a ten foot opening and let's say this side has length "x" feet.  The side opposite the side with the opening must be (x + 10) feet.  Now the other two sides of this rectangular garden are equal, so let them both equal y.  Whew!   Now, let's put that all into our first equation:150 = x + (x+10) + y + y, or to simplify140 = 2x + 2yNow maximize the area in the garden which is:A = x * y.  But, we need to get this equation in one variable (x or y), so use the first equation and solve for x:If 140 = 2x + 2y, then x = 70 - y.  Now substitute this into A = x * y.A = (70-y) * y = 70y - y^2.This is the quadratic you want to maximize.  This is simply a parabola, so find the vertex and you will have found the maximum.