Find the dimensions of a rectangle whose width is 8 miles less than its length and whose area is 84 square miles

We are going to name variables to solve the problem:

x = length

(x-8) = width

The area of the rectangle by definition is:

A = (x) * (x-8) = 84

Rewriting:

(x) * (x-8) = 84

x ^ 2-8x-84 = 0

Solving the polynomial:

(x-14) * (x + 6) = 0

x = 14

x = - 6

We need the values x> 0

Thus,

x = 14 (length)

(14-8) = 6 (wide)

Answer:

the dimensions of a rectangle are

length = 14 mi

wide = 6 mi