Question

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

Answer 1

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