Answer:
The length of the fence needed to surround this garden is [tex]188\ m[/tex]
Step-by-step explanation:
Let
x----> the length of the rectangular fence
y----> the width of the rectangular fence
we know that the area of the rectangular fence is equal to
[tex]A=xy[/tex]
[tex]A=2,184\ m^{2}[/tex]
so
[tex]2,184=xy[/tex] -----> equation A
we have
[tex]x=10+y[/tex] -----> equation B
Substitute equation B in equation A
[tex]2,184=(10+y)y[/tex]
[tex]y^{2}+10y-2,184=0[/tex]
using a graphing tool
solve the quadratic equation
The solution is [tex]y=42\ m[/tex]
see the attached figure
Find the value of x
[tex]x=10+y[/tex] ----> [tex]x=10+42=52\ m[/tex]
Find the perimeter of the rectangular fence
The perimeter is equal to
[tex]P=2(x+y)[/tex]
substitute the values
[tex]P=2(52+42)=188\ m[/tex]
