x= increased amount
L= length
W= width
The area formula is Area= L * W. Since length and width are increased, we need to increase each before adding them to the formula.
L= 12 + x
W= 14 + x
L * W= Area
(12 + x) (14 + x)= 288
multiply each parentheses
(12*14) + (12*x) + (x*14) + (x*x) = 288
168 + 12x + 14x + x^2= 288
x^2 + 26x + 168= 288
subtract 288 from both sides
x^2 + 26x - 120= 0
factor with two numbers that add to 26 and multiply to -120
(x - 4) (x + 30)= 0
set each number equal to zero
x - 4= 0
x= 4
x + 30= 0
x= -30
ANSWER: Length and width are both increased by 4 feet. -30 cannot be a solution because it is negative and we know the answer has to be a positive number.
Hope this helps! :)