Answered

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 dimensions of the new garden?

Verified Answer :

JeanaShupp

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 :-

\(\text{Area}=l\times w\\\Rightarrow\text{Area}=13\times9\\\Rightarrow\text{Area}=117\ m^2\)

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 :-

\((13+x)\cdot(9+x)=192\\\Rightarrow\ 117+x^2+22x=192\\\Rightarrow\ x^2+22x=75\\\Rightarrow\ x^2+22x-75=0\\\Rightarrow\ x^2+25x-3x-75=0\\\Rightarrow\ x(x+25)-3(x+25)=0\\\Rightarrow\ (x+25)(x-3)=0\\\Rightarrow\ x=-25\ x=3\)

Since, \(x eq-25\)

Hence, x=3

Therefore, the  dimensions of the new garden will be (13+3) m by (9+3) m=16 m by 12 m.

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