Question

Two rectangles have the same width. the length of one is 1 foot longer than the width. the length of the other is 2 feet longer than the width. the larger rectangle has 5 more square feet than the smaller. what is the width of the rectangles?

Answer 1

Rectangle 1 = w * (w+1)
Rectangle 2 = w * (w+2)

Since Rectangle 2 has 5 more square feet than rectangle 1, we can determine that :
(w * (w+2)) - 5 = w * (w+1)
w²+2w -5 = w²+w
w²+2w-5-w² = w²+w-w²
2w-5 = w
2w-5-2w = w-2w
-5 = -w
-5/-1 = -w/-1
5 = w