Arectangle with constant area has possible lengths and widths as shown in the table below. width vs. length of a rectangle width (w) length (l) 2 37.5 4 18.75 6 12.5 8 9.375 which equation can be used to find any corresponding length and width that fits the pattern in this table?

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, , the equation is of the form

 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: where l is the length and w is the width respectively;

Since, Area is constant i.e,

  ....

Therefore, the equation which is used to find any corresponding length and width that fits the pattern in this table is:    or lw = k ; where k is the constant area.

-2

7 - 9 = -2

reversed:

-2 + 9 = 7