Respuesta :
Answer:
New width of coup [tex]=14.85[/tex] feet
New length of coup [tex]=18.85[/tex] feet
Step-by-step explanation:
Width of chicken coup =[tex]10[/tex] feet
Length of chicken coup=[tex]14[/tex] feet
Area of the coup = [tex]length\times width = 10\times14=140\ ft^2[/tex]
New area is double the current area which is = [tex]2\times140=280\ ft^2[/tex]
[tex]x[/tex] is added to both length and width.
New width of coup = [tex]10+x[/tex] feet
New length of coup = [tex]14+x[/tex] feet
New area of coup can be written as = [tex]length\times width =(10+x)\times(14+x)[/tex]
So, we have
[tex](10+x)(14+x)=280[/tex]
Using FOIL method to multiply.
[tex](10\times14)+10x+14x+x^2=280\\140+24x+x^2=280[/tex]
Subtracting 280 both sides.
[tex]140+24x+x^2-280=280-280[/tex]
Rearranging terms, we have the quadratic equation to solve.
[tex]x^2+24x-140=0[/tex]
Using quadratic formula to find [tex]x[/tex]
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Plugging in values.
[tex]x=\frac{-24\pm\sqrt{24^2-(4(1)(-140))}}{2(1)}[/tex]
[tex]x = \frac{ -24\pm\sqrt{576-(-560)}}{2}\\[/tex]
[tex]x = \frac{ -24\pm\sqrt{1136}}{2}[/tex]
[tex]x = \frac{-24\pm 4\sqrt{71}}{2}[/tex]
[tex]x = \frac{-24}{2} \pm \frac{4\sqrt{71}}{2}[/tex]
[tex]\therefore x=4.8523\approx 4.85\ and\ x=-28.8523\approx -28.85[/tex]
Since [tex]x[/tex] is the length, so it cannot be negative. So [tex]x=4.85[/tex]
New width of coup = [tex]10+x=10+4.85=14.85[/tex] feet
New length of coup = [tex]14+x=14+4.85=18.85[/tex] feet
