Answer:
12 miles by 8 miles
Step-by-step explanation:
Let length be represented by x
Since width is 4 miles less than the length, therefore, the width will be (x-4) miles
Area=Length*Width
Area=x(x-4)=[tex]x^{2}-4x[/tex]
Area is given hence
[tex]x^{2}-4x=96[/tex]
To write the above equation as a quadratic equation
[tex]x^{2}-4x-96=0[/tex]
By factorization, we find two numbers whose sum is -4 and product is -96, these are 8 and -12. Therefore, taking these two numbers back to our equation
(x+8)(x-12)=0
Therefore, x=-8 or 12
Equally, using quadratic formula of
[tex]x=\frac{-b±\sqrt{b^{2} -4ac}}{2a}[/tex] for equation [tex]ax^{2}+bx+c=0[/tex] and in our case a=1, b=-4 and c=-96
[tex]x=\frac{4±\sqrt{(-4)^{2} -(4*1*-96)}}{2*1}[/tex]
x=-8 or 12
Since length can't be negative, hence x=12
The length is 12 miles
Width=12-4=8 miles
Dimensions: 12 miles by 8 miles
