Question

A square garden plot measures 180 square feet. A second square garden plot measures 320 square feet. How many more feet of fence will the second garden plot require over that required for the first garden plot?

Answer 1

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,

$A_1=x^2\\180=x^2\\Taking\ square\ root\ on\ both\ sides\\\sqrt{180}=\sqrt{x^2}\\x=\sqrt{2*2*3*3*5}\\x=\sqrt{2^2*3^2*5}\\x=2*3\sqrt{5}\\x=6\sqrt{5}$

For second square:

Let y be the side of second square

$A_2=y^2\\320=y^2\\Taking\ square\ root\ on\ both\ sides\\\sqrt{320}=\sqrt{y^2}\\y=\sqrt{2*2*2*2*2*2*5}\\y=\sqrt{2^2*2^2*2^2*5}\\y=2*2*2\sqrt{5}\\y=8\sqrt{5}$

Perimeter of First Square:

$P_1=4x\\=4(6\sqrt{5})\\=24\sqrt{5}\ feet$

Perimeter of Second Square:

$P_2=4y\\=4(8\sqrt{5})\\=32\sqrt{5}\ feet$

The smaller perimeter will be subtracted from larger perimeter to find that how much more fence will be needed.

$P_2-P_1=32\sqrt{5}-24\sqrt{5}\\=(32-24)\sqrt{5}\\=8\sqrt{5}\ feet$

The second garden plot will require 8√5 feet more fence than the first garden plot.

Keywords: Radicals, Operations on Radicals

Learn more about radicals at:

• brainly.com/question/13219835
• brainly.com/question/1836777

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