Problema Solution
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 4 more square feet than the smaller. What is the width of the rectangles?
Answer provided by our tutors
let
w = the width of the rectangles (since they have the same width)
l1 = the length of the first rectangle
l2 = the length of the second rectangle
the length of one is 1 foot longer than the width
l1 = w + 1
the length of the other is 2 feet longer than the width
l2 = w + 2 > w + 1 = l1 thus the second rectangle is the larger
the larger rectangle has 4 more square feet than the smaller
l2*w = l1*w + 4
if we plug the values for l1 and l2 in the last equation we get
(w + 2)w = (w + 1)w + 4
by simplifying and solving we find
w = 4 ft
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the width of the rectangles is 4 feet.