Answer:
8 feet
Step-by-step explanation:
Given: the area of a rectangular wall of barn is 160 square feet. its length is 4 feet longer than twice its width.
To Find: the width of the wall of the barn
Solution:
Area of rectangular wall of barn \(=160\) \(\text{sq.feet}\)
Let the length of wall of barn is \(=\text{l}\)
Let the width of wall of barn is \(=\text{b}\)
now,
length of wall of barn is, \(\text{l}=2\text{b}+4\)
Area of wall of barn \(=\text{length}\times\text{width}\)
\(=\text{l}\times\text{b}\)
\((2\text{b}+4)\text{b}\)
\((2\text{b}+4)\text{b}=160\)
\(2\text{b}^2+4\text{b}=160\)
\(\text{b}^2+2\text{b}=80\)
\(\text{b}^2+2\text{b}-80=0\)
on factorizing
\((\text{b}+10)(\text{b}-8)=0\)
as width cannot be less than zero,
\(\text{b}=8\) \(\text{feet}\)
Width of the wall of barn is \(8\) \(\text{feet}\)
