The second garden plot will require 8√5 feet more fence than the first garden plot.
Further explanation:
In order to find the fence, we have to find the perimeter of both squares
So,
Area of Square 1: A1=180 square feet
Area of Square 2: A2=320 Square feet
Let x be the side of square 1:
Then,
[tex]A_1=x^2\\180=x^2\\Taking\ square\ root\ on\ both\ sides\\\sqrt{180}=\sqrt{x^2}\\x=\sqrt{2*2*3*3*5}\\x=\sqrt{2^2*3^2*5}\\x=2*3\sqrt{5}\\x=6\sqrt{5}[/tex]
For second square:
Let y be the side of second square
[tex]A_2=y^2\\320=y^2\\Taking\ square\ root\ on\ both\ sides\\\sqrt{320}=\sqrt{y^2}\\y=\sqrt{2*2*2*2*2*2*5}\\y=\sqrt{2^2*2^2*2^2*5}\\y=2*2*2\sqrt{5}\\y=8\sqrt{5}[/tex]
Perimeter of First Square:
[tex]P_1=4x\\=4(6\sqrt{5})\\=24\sqrt{5}\ feet[/tex]
Perimeter of Second Square:
[tex]P_2=4y\\=4(8\sqrt{5})\\=32\sqrt{5}\ feet[/tex]
The smaller perimeter will be subtracted from larger perimeter to find that how much more fence will be needed.
[tex]P_2-P_1=32\sqrt{5}-24\sqrt{5}\\=(32-24)\sqrt{5}\\=8\sqrt{5}\ feet[/tex]
The second garden plot will require 8√5 feet more fence than the first garden plot.
Keywords: Radicals, Operations on Radicals
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