Adina has a rectangular garden that measures 9 m wide by 13 m long. She wants to increase the area to 192 m² by increasing the width and length by the same amount.

What will be the length (longer dimension) of the new garden?

A=LW and we wish to increase L and W by the same amount to get an area of 192m^2.

(9+2x) (13+2x) = 192

117+18x+26x+4x^2=192

4x^2+44x+117=192

4x^2+44x=75

x^2+11x=18.75

(x+5.5) ^2=30.25+18.75

(x+5.5) ^2=49

x+5.5=±7

x=-5.5±7, since x>0

x=1.5

13+2 (1.5)

16 meters will be the new longer dimension.