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#### Algebra Solutions

##### Topics || Problems

After plowing a border inside a rectangular field 60 rods wide and 80 rods long, a farmer finds that one half of the field remains to be plowed. How wide is the border?

The area of the rectangular field is $$60x80 = 4800$$. 

After the farmer plowed the borders, the unplowed dimension would be: width = $$60-2x$$ and length = $$80-2x$$, where $$x$$ is the width of the boder

Thus, $$4800 = 2(60-2x)(80-2x)$$

$$4800 = 2(4800 - 280x + 4x^2)$$

$$0 = 4800 -560x + 8x^2$$

$$x_1 = \frac{560 + \sqrt{560^2 -4(8)(4800)}}{16}$$

$$x_1 = 60$$

$$x_2 = \frac{560 - \sqrt{560^2 -4(8)(4800)}}{16}$$

$$x_2 = 10$$

By checking the values of $$x's$$ the width of the border is $$10$$ rods.