Question

A rectangle 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?

Answer 1

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, $y \propto \frac{1}{x}$ , the equation is of the form

$b= \frac{k}{a}$  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: $A =lw$ where l is the length and w is the width respectively;

Since, Area is constant i.e,

$A = 2 \times 37.5 = 75$

 $A = 4 \times 18.75 = 75$ ....

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

Answer 2

The answer is. A) I= k/w Where I is the length, w is the width, and k is a constant