You could use a proportion and cross-multiply. For example, if the reduced rectangle had a length of 3 and a width of 5, and then the one measurement of the original rectangle is length of 7, you could set a proportion like: 3/5 = 7/x
Then, cross multiply to solve for x, and that sound give the missing measure.
Using the given measurements of both figures, set up a proportion that has the corresponding parts in the same position. Then solve the proportion using cross products to find the value for the unknown.