Arectangle 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?

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! :)