Question

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Answer 1

Answer:

New width of coup $=14.85$ feet

New length of coup $=18.85$ feet

Step-by-step explanation:

Width of chicken coup =$10$ feet

Length of chicken coup=$14$ feet

Area of the coup = $length\times width = 10\times14=140\ ft^2$

New area is double the current area which is = $2\times140=280\ ft^2$

$x$ is added to both length and width.

New width of coup = $10+x$ feet

New length of coup = $14+x$ feet

New area of coup can be written as = $length\times width =(10+x)\times(14+x)$

So, we have

$(10+x)(14+x)=280$

Using FOIL method to multiply.

$(10\times14)+10x+14x+x^2=280\\140+24x+x^2=280$

Subtracting 280 both sides.

$140+24x+x^2-280=280-280$

Rearranging terms, we have the quadratic equation to solve.

$x^2+24x-140=0$

Using quadratic formula to find $x$

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Plugging in values.

$x=\frac{-24\pm\sqrt{24^2-(4(1)(-140))}}{2(1)}$

$x = \frac{ -24\pm\sqrt{576-(-560)}}{2}$

$x = \frac{ -24\pm\sqrt{1136}}{2}$

$x = \frac{-24\pm 4\sqrt{71}}{2}$

$x = \frac{-24}{2} \pm \frac{4\sqrt{71}}{2}$

$\therefore x=4.8523\approx 4.85\ and\ x=-28.8523\approx -28.85$

Since $x$ is the length, so it cannot be negative. So $x=4.85$

New width of coup = $10+x=10+4.85=14.85$ feet

New length of coup = $14+x=14+4.85=18.85$ feet