Answer :
To solve this equation, we remember that perimeter p=16 in, and p=2L+2W. Replacing for p and using the distributive property in reverse, we can let our equation look like 16=2(L+W). Divide both sides by 2 to isolate the variables; our equation is now 8=L+W. From here, L, or the value of the rectangle's length, may be any value between 1 and 7, provided that the width W sums with it to make 8. For example, L could be 5 and W 3, and all would work out; any combination of 1-7, 2-6, 3-5, and 4-4 (a square) are possible combinations of the rectangle's side lengths. Obviously, a side length for a rectangle cannot be negative and cannot be 0, which is why our set of solutions is so small. For greater confidence, one can go back to the original equation and test the solution by plugging values into the formula. For example, 16=2(5)+(2)3 --> 16=10+6 --> 16=16. All good! If you're being really technical about the definitions of length vs. width, then you might need to stipulate that the length should always be the longer side, meaning that your set of results for L would only be {4,5,6,7}. A square is a rectangle, so the 4 value should be valid.
