Respuesta :
The answer is. A) I= k/w Where I is the length, w is the width, and k is a constant
Answer:
Given: A rectangle with constant area has possible lengths and width as shown in the given table.
Inverse variation states that a relationship between two variables in which the product is a constant.
If one variable increases, the other decreases in proportion so that the product is unchanged.
i.e, if b is inversely proportional to a i.e, [tex]y \propto \frac{1}{x}[/tex] , the equation is of the form
[tex]b= \frac{k}{a}[/tex] or ab = k , where k is constant of variation.
As, you can see from the table as width(w) increases, the length decreases so ,it is an inverse variation.
By area of rectangle formula: [tex]A =lw[/tex] where l is the length and w is the width respectively;
Since, Area is constant i.e,
[tex]A = 2 \times 37.5 = 75[/tex]
[tex]A = 4 \times 18.75 = 75[/tex] ....
Therefore, the equation which is used to find any corresponding length and width that fits the pattern in this table is: [tex]l = \frac{k}{w}[/tex] or lw = k ; where k is the constant area.
