Answer:
The constant of variation is 4032
Step-by-step 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) =[tex]l \times w[/tex] = [tex]72 \times 56[/tex] = 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 = [tex]l \times w[/tex] = [tex]l \times 21[/tex]
From [1];
4032 = [tex]l \times 21[/tex]
Divide 21 both sides we get;
[tex]l =\frac{4032}{21} = 192[/tex] cm
therefore, the length of rectangle B is 192 cm
To find the constant variation:
if y varies inversely as x
i.e, [tex]y \propto \frac{1}{x}[/tex]
⇒ [tex]y = \frac{k}{x}[/tex] 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: [tex]l \propto \frac{1}{w}[/tex]
or [tex]l = \frac{A}{w}[/tex] where A is the constant of variation
Since, the area (A) of both the rectangles are constant.
therefore, the constant of variation is, 4032
