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Dahasolnce [82]
3 years ago
12

Scratchpad

Mathematics
1 answer:
natulia [17]3 years ago
6 0

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

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