# Quadratic Equations Word Problems : Maximizing Area

Amanda has 300 feet of lumber to frame a rectangular patio. She wants to maximize the area of her patio. What should the dimensions of the patio be, and show how the maximum area of the patio is calculated from the algebraic equation by using the vertex form to find the maximum. Show the work when computing this equation.

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#### Solution Preview

Solution. Let us assume the length and width of a rectangular patio are x and y, respectively. By given information, we have

2(x+y)=300

i.e.,

x+y=150 ...

#### Solution Summary

Area is maximized by solving a quadratic equation. The solution is detailed and well presented.

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