Question 1195712
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The response from the other tutor shows a good typical formal algebraic method for solving the problem.<br>
But you can also get good experience in problem solving by using logical reasoning and a bit of simple arithmetic.<br>
If the dimensions of the room are 21 by 28 feet and the strip surrounding the rug is of uniform width, then the dimensions of the rug are 21-x and 28-x feet.  The numbers given in the problem are whole numbers, so the solution will almost certainly involve whole numbers.  So subtract whole numbers from each dimension of the room to find a pair of numbers whose product is 494.<br>
Subtracting 1 from each dimension gives us 27 by 20 feet; that product is obviously not 494.<br>
Subtracting 2 from each dimension gives us 26 by 19 feet.  The units digit of that product is 4 (9 times 6 is 54), so that could be our answer. And, multiplying, we find that indeed 26*19 is 494.  So the dimensions of the rug are 26 by 19 feet.<br>
ANSWER: 26 feet by 19 feet<br>