Question

Marielle's painting has the dimensions shown. The school asks her to paint a larger version that will hang in the cafeteria. The length of the larger version is tripled, and its width is tripled as well. Is the area of the original painting proportional to the area of the larger painting? If so, what is the constant of proportionality?

Answer 1

Answer:

because of ratio of areas of two

Answer 2

Tip:

• Area of rectangle=$length\times width$

Explanation:

• Marielle's painting is rectangular in shape. For making a large painting she tripled the length and width of her original painting.
• We have to find the constant of proportionality.
• We will first find the area of original painting and then of larger painting and find the ratio between them.

Step

Step 1 of 2:

Length of original painting $= x~cm$

Width of original painting $=y~cm$

Area of original painting = $length\times width$

                                         $=xy~cm^2$

Length of larger painting $=3x~cm$

Width of larger painting $=3y~cm$

Area of larger painting $=9xy~cm^2$

Step 2 of 2:

Area of larger painting $=9xy~cm^2$

Area of larger painting $=$ $9$ Area of original painting   (∵ Area of original painting$=xy~cm^2$)

So, The area of the original painting is proportional to the area of the larger painting and the proportionality constant is $9$.              

Final Answer:

The constant of proportionality is $9$.