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. What is the constant of variation?

Answer 1

The constant of variation is 4032

Explanation:

Given:

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

Area of rectangle is multiply its length by its width.

Then,

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

It is given that the other rectangle B has the same area as the rectangle A.

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

First find the length of rectangle B:

Given: width of the rectangle B is 21 cm

then, by definition

Area of rectangle B = =

From [1];

4032 =

Divide 21 both sides we get;

cm

therefore, the length of rectangle B is 192 cm

To find the constant variation:

if y varies inversely as x

i.e,

⇒ where k is the constant variation.

or k = xy

As area of rectangle is multiply its length by width.

This is the inversely variation.

as:

or where A is the constant of variation

Since, the area (A) of both the rectangles are constant.

therefore, the constant of variation is, 4032

Answer 2

The constant of variation is 4032

Explanation:

Given:

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

Area of rectangle is multiply its length by its width.

Then,

area of rectangle (A) =
`l * w` =
`72 * 56` = 4,032 square cm.

It is given that the other rectangle B has the same area as the rectangle A.

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

First find the length of rectangle B:

Given: width of the 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 =(4032)/(21) = 192` cm

therefore, the length of rectangle B is 192 cm

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 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

Since, the area (A) of both the rectangles are constant.

therefore, the constant of variation is, 4032