Question

3. Two mathematicians are neighbors. Each owns a separate rectangular plot of land that shares a boundary and has the

same dimensions. They agree that each has an area of 2x2 + 3x + 1 square units. One mathematician sells his plot to
the other. The other wants to put a fence around the perimeter of his new combined plot of land. How many linear
units of fencing does he need? Write your answer as an expression in x.

Answer 1

• shared short side: 10x +6
• shared long side: 8x +6

Explanation:

The factors of the given polynomial are (2x+1) and (x+1). We presume these are the side lengths of each rectangular plot. If the short side (x+1) was common, then the perimeter of the combined lot is ...

4(2x+1) +2(x +1) = 10x +6 . . . units of fence for short side common

If the long side (2x+1) was common, then the perimeter of the combined lot is ...

4(x+1) +2(2x+1) = 8x +6 . . . units of fence for long side common