Question

Find the dimensions of a rectangle whose width is 7 miles less than its length and whose areas is 78 square miles.

Answer 1

W = L - 7
WL = 78

(L-7)L = 78

L^2 - 7L - 78 = 0
Factorize: (L-13)(L+6) = 0

L = 13 or -6

A length cannot be negative, so the length must be 13 miles.
The width is 13-7 = 6 miles.