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Answer: 16 m by 12 m.
Step-by-step explanation:
Given: The length of garden l = 13 m
The width of the garden w= 9 m
The area of the rectangular garden is given by :-
[tex]\text{Area}=l\times w\\\Rightarrow\text{Area}=13\times9\\\Rightarrow\text{Area}=117\ m^2[/tex]
It she wants to increase the garden, the dimensions of the new garden will be (13+x) m by (9+x) m , then according to the question we have :-
[tex](13+x)\cdot(9+x)=192\\\Rightarrow\ 117+x^2+22x=192\\\Rightarrow\ x^2+22x=75\\\Rightarrow\ x^2+22x-75=0\\\Rightarrow\ x^2+25x-3x-75=0\\\Rightarrow\ x(x+25)-3(x+25)=0\\\Rightarrow\ (x+25)(x-3)=0\\\Rightarrow\ x=-25\ x=3[/tex]
Since, [tex]x\neq-25[/tex]
Hence, x=3
Therefore, the dimensions of the new garden will be (13+3) m by (9+3) m=16 m by 12 m.