Answer: The constant of variation is 4032.
Explanation:
It is given that a rectangle has length 72 cm and it’s width 56 cm. The other rectangle has the same area as this one, but its width is 21 cm.
In joint variation there are two quantities like,
[tex]A=l\times w[/tex]
Where, l is length and w is width.
We want to find the constant of variation, so we have to find the length.
Area of first rectangle is,
[tex]A=72\times 56=4032[/tex]
Area of second triangle is,
[tex]A=l\times 21=21l[/tex]
It is given that the area of both triangles are equal.
[tex]l\times 21=4032[/tex]
[tex]l=192[/tex]
So the length of the second rectangle is 192 cm.
[tex]y\propto \frac{1}{x}[/tex]
[tex]y=\frac{k}{x}[/tex]
Then k is the constant of variation.
Since area if the product of length and breadth.
[tex]w\propto \frac{1}{l}[/tex]
[tex]w=\frac{A}{l}[/tex]
Therefore A is the constant of variation. Since the area of both rectangles are same, therefore the constant of variation is 4032.
