Casey has a rectangular garden that measures 9 m wide by 13 m long. She wants to increase the area to 192 m^2 by increasing the width and same amount. What will be the width (shorter dimension) of the new garden.

here your problem can be modeled by the subsequent equation:

(9 + r)(13+r) = 192, where r is the requested increment

then we have to solve the subsequent quadratic equation:

r^2 + 22r - 75 =0

so the unique acceptable solution is r=3

then the new dimensions are:

9 + 3= 12

13 + 3= 16

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