Respuesta :
Answer:
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 [tex]A = l \times w[/tex]
Then;
area of rectangle (A) =[tex]l \times w = 72 \times 56[/tex] = 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 = [tex]l \times w = l\times 21[/tex]
From [1];
4032 = [tex]l \times 21[/tex]
Divide 21 both sides we get;
[tex]l = \frac{40321}{21} = 192 cm[/tex]
then; the length of rectangle B is 192 cm
Now,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 we know that 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
As it is given in the statement that area (A) of both the rectangles are constant.
therefore, the constant of variation is, 4032
