Answer:
length = 12 miles
width = 6 miles
Explanation:
Framing algebraic expression and solving:
length = x miles
width = (x - 6) miles
Area of rectangle = 72 square miles
length * width = 72
x * (x - 6) = 72
x*x - 6*x = 72
x² - 6x - 72 = 0
Sum = -6
Product = -72
Factors = 6 , (-12) { 6 + (-12) = -6 and 6*(-12) =-72 }
Rewrite the middle term using the factors.
x² + 6x - 12x - 72 = 0
x(x + 6) -12(x + 6) =0
(x + 6)(x - 12) = 0
{x + 6 = 0 is rejected as length will not have negative value}
x - 12 = 0
length = 12 miles
Width = 12 - 6 = 6 miles