A rectangular deck is 12 ft by 14 ft. When the length and width are increased by the same amount, the area becomes 288 sq. ft. By how much were the dimensions increased?

Let x be the amount added to each dimension. The new area is (12 + x)(14 + x) = 288. Expanding and solving gives x² + 26x − 120 = 0, which factors as (x + 30)(x − 4) = 0. Since the increase must be positive, x = 4 ft, so the dimensions were increased by 4 ft.

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