Answer:
The length of fencing will be [tex]300\ ft[/tex]
Step-by-step explanation:
Step 1
Find the dimensions of the rectangle
we know that
The area of a rectangle is equal to
[tex]A=bh[/tex]
In this problem we have
[tex]A=5,000\ ft^{2}[/tex]
so
[tex]5,000=bh[/tex] -----> equation A
[tex]b=\frac{h}{2}[/tex] -----> equation B
Substitute equation B in equation A
[tex]5,000=(\frac{h}{2})h[/tex]
[tex]10,000=h^{2}[/tex]
square root both sides
[tex]h=100\ ft[/tex]
Find the value of b
[tex]b=\frac{h}{2}[/tex] -----> [tex]b=\frac{100}{2}=50\ ft[/tex]
step 2
Find the length of fencing
The perimeter of a rectangle is equal to
[tex]P=2(b+h)[/tex]
we have
[tex]h=100\ ft[/tex]
[tex]b=50\ ft[/tex]
substitute
[tex]P=2(50+100)=300\ ft[/tex]
