Arectangle has length 72 cm and width 56 cm. the other rectangle has the same area as this one, but its width is 21 cm. b find the constant of variation.

Constant of Variation is, 4032

Explanation:

Let a rectangle (say A) has length of rectangle(l)= 72 cm and width of rectangle(w) = 56 cm.

Since, Area of rectangle is multiply its length by its width.

i,e

Then;

area of rectangle (A) = = 4,032 square cm.

It is also given that the other rectangle (let B) has the same area as the rectangle A.

So, the area of rectangle (B)= area of rectangle (A) = 4,032 square cm.  .......[1]

First calculate the length of rectangle B:

Given: The width of rectangle B is 21 cm

then, by definition

Area of rectangle B =

From [1];

4032 =

Divide 21 both sides we get;

then; the length of rectangle B is 192 cm

Now,to find the constant variation:

if y varies inversely as x

i.e,

⇒  ;  where k is the constant variation.

or k = xy

As we know that area of rectangle is multiply its length by width.

This is the inversely variation.

as:  

or

 ;where A is the constant of variation

As it is given in the statement that area (A) of both the rectangles are constant.

therefore, the constant of variation is, 4032

hello i am doing good for you that it's summer in your country or state ; )

btw in my country we just have sun and rain as (because i live in the caribbean lol)

also, thx a lot for the points : )