The key to solving any word problem is identifying what is unknown, what is known, and what equations must be used. Once these components are identified, it is simply a matter of filling in the blanks. Word problems involving polynomials are no different than any other mathematical word problem in this regard.
- Determine what is unknown and known
For example, if asked to find the perimeter of a rectangle whose area is equal to 55 square meters and whose length is 1 meter less than twice the width, the unknown is the width. The width can be assigned the variable x. The known variables in this problem are the area and length. The reason the length is considered a known is because it is directly related to the width. The length can be expressed as 2x - 1.
- Determine any equations to be used
Although the problem is asking for the perimeter, the equation for perimeter cannot be used to determine the value of x since it has two unknowns. However, the area is known, so the equation for the area must be used.
- Plug in values, and solve for x
Once the variables for width and length are plugged into the equation for the area, 55 = (2x - 1) * x, solve for x. The value of x is 5.5. Using this value for x, plug it into the equation for the perimeter, P = 2 * ((2x-1) + x). The perimeter of this rectangle is therefore 31 meters.