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

c.

step-by-step explanation:

because first you have to add the 4x, 9x, and the 7x together and you get 20x and then you add the last numbers up and you get 5and then you put the subtraction sign in there and that's how you get the answer.