Respuesta :
Answer
Find out the what is the constant proportionality .
To prove
Formula
Area of rectangle = Length × Breadth
As given
Marielle’s painting has the dimensions shown (Painting Width = 18 inches, Painting Length = 24 inches).
Area of the original painting = 18 × 24
= 432 inches²
As given
The school asks her to paint a larger version that will hang in the cafeteria.
The larger version will be twice the width and twice the height.
Length of the larger version painting = 2 × 18
= 36 inches
Breadth of the larger version painting = 2 × 24
= 48 inches
Now area of the larger version painting = 36 × 48
= 1728 inches²
As given
The area of the original painting proportional to the area of the larger
painting .
Thus
[tex]Area\ of\ original\ painting\ \propto\ Area\ of\ larger\ painting[/tex]
[tex]Area\ of\ original\ painting\ = k\times \ Area\ of\ larger\ painting[/tex]
Where k is the constant of proportionality
Putting the value
432 = k × 1728
[tex]k = \frac{1728}{432}[/tex]
k = 4
The constant proportionality is 4 .
Hence proved
