Answer:
Therefore, he must buy [tex]280[/tex] feet of fence to form barn if the perimeter of the rectangle is [tex]320[/tex] feet.
Step-by-step explanation:
Considering '[tex]x[/tex]' be the width of the rectangle
- As the barn forms one end of the rectangle and the length of the rectangle is three times the width.
so
Length of the rectangle [tex]= 3x[/tex]
as
[tex]Perimeter\:of\:rectangle\:=\:2\left(l\times \:w\right)[/tex]
[tex]320 =2(x+ 3x)[/tex]
[tex]2\left(x+3x\right)=320[/tex]
[tex]\frac{2\left(x+3x\right)}{2}=\frac{320}{2}[/tex]
[tex]4x=160[/tex]
[tex]x=40[/tex]
Hence, the width of the rectangular area is [tex]40 feet[/tex] .
and
Length of the rectangle [tex]= 3x[/tex]
= 3 × 40
=120 feet
As it is clear that the barn makes one end of the rectangle.
[tex]\left(2\times \:l\right)+w[/tex]
[tex]=\left(2\times 120\right)+40[/tex]
[tex]=\left(2\times 120\right)+40[/tex]
[tex]=280[/tex]
Therefore, he must buy [tex]280[/tex] feet of fence to form barn if the perimeter of the rectangle is [tex]320[/tex] feet.
