Respuesta :
Answer:
The number of feet by which the length and width is increased is:
3.14 feet
Step-by-step explanation:
Giovanni has a dog enclosure that is 6 feet by 10 feet in his backyard.
The area of the enclosure is: 6×10=60 square feet
Now let x be the amount by which the length and width of the enclosure is increased.
i.e. the length is: 6+x
and width is: 10+x
Also, the new area of the enclosure is:
[tex](6+x)\cdot (10+x)=2\times 60\\\\\\i.e.\\\\\\x^2+16x+60=120\\\\\\i.e.\\\\\\x^2+16x+60-120=0\\\\\\i.e.\\\\\\x^2+16x-60=0[/tex]
On solving using the quadratic formula
( i.e. any quadratic equation of the type:
[tex]ax^2+bx+c=0[/tex]
the solution is given by:
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex] )
Here we have: a=1 and b=16 and c= -60
We get the solution as:
[tex]x=\dfrac{-16\pm \sqrt{(16)^2-4\times (-60)\times 1}}{2}\\\\\\x=\dfrac{-16\pm \sqrt{256+240}}{2}\\\\\\x=\dfrac{-16\pm \sqrt{496}}{2}\\\\\\x=\dfrac{-16\pm 22.2710}{2}[/tex]
i.e. [tex]x=-19.136\ and\ x=3.136[/tex]
x can't be negative as it is the amount of distance.
Hence, to the nearest hundredth we have:
x=3.14
Hence, the answer is:
3.14 feet
