Question

find the dimensions of a rectangle whose width is 4 miles less than its length and whose area is 96 square miles

Answer 1

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)=$x^{2}-4x$

Area is given hence

$x^{2}-4x=96$

To write the above equation as a quadratic equation

$x^{2}-4x-96=0$

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

$x=\frac{-b±\sqrt{b^{2} -4ac}}{2a}$ for equation $ax^{2}+bx+c=0$ and in our case a=1, b=-4 and c=-96

$x=\frac{4±\sqrt{(-4)^{2} -(4*1*-96)}}{2*1}$

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