Respuesta :
Answer:
Length = 17 feet, Width = 5 feet
Step-by-step explanation:
Given:
The area of a rectangular wall of a barn is 85 square feet.
Its length is 12 feet longer than the width.
Question asked:
Find the length and width of the wall of the barn.
Solution:
Let width of a rectangular wall of a barn = [tex]x[/tex]
As length is 12 feet longer than the width.
Length of a rectangular wall of a barn = [tex]12+x[/tex]
As we know:
[tex]Area\ of\ rectangle=length\times breadth[/tex]
[tex]85=(12+x)x\\\\85=12x+x^{2} \\[/tex]
Subtracting both sides by 85
[tex]x^{2} +12x-85=0\\x^{2} +17x-5x-85=0\\Taking\ common\\x+(x+17)-5x(x+17)=0\\(x+17)(x-5)=0\\x+17=0, x-5=0\\x=-17,x=5[/tex]
As width can never be in negative, hence width of a rectangular wall of a barn = [tex]x[/tex] = 5 feet
Length of a rectangular wall of a barn = [tex]12+x=12+5=17\ feet[/tex]
Therefore, length and width of the wall of the barn is 17 feet and 5 feet respectively.
