To find: A function that models perimeter in terms of sides.

Question

To find:  A function that models perimeter in terms of sides.

yunitsiL · Accepted Answer

The model we want is a function that gives the perimeter of the rectangle.
For the rectangle,
$P e r i m e t e r = 2 (L e n g t h) + 2 (W i d t h)$
There are two varying quantities: Length and width.
The function we want depends on its length x.
We must express the width in terms of its length x. If we let width of the rectangle be y and area of the rectangle is $16 m^{2}$ then we have,
$x y = 16$
Divide by x,
$y = \frac{16}{x}$
The model is the function P that gives the perimeter of the rectangle for any length x.
$P e r i m e t e r = 2 (L e n g t h) + 2 (W i d t h)$
$P (x) = 2 x + 2 (\frac{16}{x})$
$= 2 x + \frac{32}{x}, x > 0$
Thus, the perimeter of the rectangle modeled by the function
$P (x) = 2 x + \frac{32}{x}, x > 0$ .
Final statement:
The perimeter of the rectange modeled by the function $P (x) = 2 x + \frac{32}{x}, x > 0$ .

To find: A function that models perimeter in terms of sides.

Answered question

Answer & Explanation

New Questions in Algebra II