Question

A rectangle 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.

Answer 1

Constant of Variation is, 4032

Step-by-step 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
`A = l * w`

Then;

area of rectangle (A) =
`l * w = 72 * 56` = 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 =
`l * w = l* 21`

From [1];

4032 =
`l * 21`

Divide 21 both sides we get;

`l = (40321)/(21) = 192 cm`

then; the length of rectangle B is 192 cm

Now,to find the constant variation:

if y varies inversely as x

i.e,
`y \propto (1)/(x)`

⇒
`y = (k)/(x)`; 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:
`l \propto (1)/(w)`

or

`l = (A)/(w)` ;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