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#### Algebra Solutions

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A rectangular plot of ground is 120 yards long and 80 yards wide. To double the area of the plot, while retaining the rectangular shape, strips of equal width will be added at one end and along one side. Find the width of the strip.

Let $$x$$ be the width of the strip. Thus the new length of the rectangle is $$120 + x$$ and the new width is $$80+x$$.

The area of the old plot: $$A_o = 120x80 = 9600 yd^3$$

The area of the new plot is twice the rea of the old plot. Thus, $$A_n = 2A_o$$

$$A_n = (120 +x)(80+x)$$

$$A_n =9600 + 200x + 80x^2$$

p>$$9600 + 200x + 80x^2 = 2(9600)$$

$$x^2 + 200 x -9600 = 0$$

$$x = \frac{-200+\sqrt{200^2 - 4(1)(-9600)}}{2(1)}$$

$$x = 40~yards$$Answer