1. ## polynomials...Help

Find a polynomial for the perimeter and for the area(Do not factor)
the given sides of the rectangle are z+4 for one side an z for the other
for the perimeter I got z(z+4)
for the area I have z^2 +4z + 16

I have no clue, if this is wrong? is someone willing to guide me Please, with the steps?

2. Originally Posted by NotThatGood
Find a polynomial for the perimeter and for the area(Do not factor)
the given sides of the rectangle are z+4 for one side an z for the other
for the perimeter I got z(z+4)
for the area I have z^2 +4z + 16

I have no clue, if this is wrong? is someone willing to guide me Please, with the steps?
Okay, HOW did you get those answers? If your text book has a problem like this surely it has formulas for perimeter and area. Did you look at them?

The "perimeter" is the total distance around the rectangle. Imagine drawing a large rectangle on the ground and actually measuring the distances. There are, of course, 4 sides, 2 with length z and 2 with length z+ 4. You might first measure the length z, then the length z+ 4 and add them to get the length around those first two sides, then add the third side, another z, and finally, the fourth side, another z+ 4. The total distance is the sum of those: z+ z+4+ z+ z+ 4 which is also equal to 2z+ 2(z+ 4) or 4z+ 8.

Notice this does NOT involve multiplying two lengths together. That is
because "perimeter" is a distance measure. If the sides were measured in meters, then the perimeter is measured in distance also. If we multiplied two lengths together, the units would be "$\displaystyle meters^2$" or "square meters", an area measurement. In fact, the area of this rectangle is the product of the two side lengths, z(z+4), what you used for "perimeter".

I'm not sure how you got $\displaystyle z^2+ 4z+ 16$. Perhaps you were thinking of the area of a square, $\displaystyle s^2$ and were trying to do $\displaystyle (z+4)^2$. But that, of course, ignores the length "z". And, if that was what you were trying to do, you multiplied wrong: $\displaystyle (z+ 4)^2= z^2+ 8z+ 16$.