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

Dimensions of rectangle = 12 + x and 14 + x

(12 + x) (14 + x) = 288

x^2 + 26x + 168 = 288

x^2 + 26x - 120 = 0

(x + 30) (x - 4) = 0

x=-30, x = 4

since 4 is positive

the dimensions increased by 4 feet

check the answer

12+4 = 16

14 + 4 = 18

18*16 = 288

Its 16 by 18 so by 4 ft