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 [tex]=160[/tex] [tex]\text{sq.feet}[/tex]
Let the length of wall of barn is [tex]=\text{l}[/tex]
Let the width of wall of barn is [tex]=\text{b}[/tex]
now,
length of wall of barn is, [tex]\text{l}=2\text{b}+4[/tex]
Area of wall of barn [tex]=\text{length}\times\text{width}[/tex]
[tex]=\text{l}\times\text{b}[/tex]
[tex](2\text{b}+4)\text{b}[/tex]
[tex](2\text{b}+4)\text{b}=160[/tex]
[tex]2\text{b}^2+4\text{b}=160[/tex]
[tex]\text{b}^2+2\text{b}=80[/tex]
[tex]\text{b}^2+2\text{b}-80=0[/tex]
on factorizing
[tex](\text{b}+10)(\text{b}-8)=0[/tex]
as width cannot be less than zero,
[tex]\text{b}=8[/tex] [tex]\text{feet}[/tex]
Width of the wall of barn is [tex]8[/tex] [tex]\text{feet}[/tex]
