Ariana is painting a rectangular canvas. The total area of the canvas is 36 square inches. She will paint a 3 inch by 4 inch part of the blue. She will paint the rest of the canvas yellow. What are possible dimensions of the part of the canvas She will paint yellow?
Let's say the length and width of the part of the canvas Ariana will paint yellow are L and W inches respectively.
We know the total area of the canvas is the sum of the areas of the blue part and the yellow part, which is 36 square inches.
So, we have the equation L * W + 3 * 4 = 36.
Simplifying the equation, we get L * W = 24.
Now, let's list down the possible dimensions of the part of the canvas she will paint yellow.
If L = 1 inch and W = 24 inches, then the area would be 24 square inches, which is not possible since the area needs to be 24 square inches.
If L = 2 inches and W = 12 inches, then the area would be 24 square inches, which matches the condition.
If L = 3 inches and W = 8 inches, then the area would be 24 square inches, which matches the condition.
If L = 4 inches and W = 6 inches, then the area would be 24 square inches, which matches the condition.
If L = 6 inches and W = 4 inches, then the area would be 24 square inches, which matches the condition.
If L = 8 inches and W = 3 inches, then the area would be 24 square inches, which matches the condition.
If L = 12 inches and W = 2 inches, then the area would be 24 square inches, which matches the condition.
If L = 24 inches and W = 1 inch, then the area would be 24 square inches, which is not possible since the area needs to be 24 square inches.
Therefore, the possible dimensions of the part of the canvas Ariana will paint yellow are 2 inches by 12 inches, 3 inches by 8 inches, 4 inches by 6 inches, 6 inches by 4 inches, 8 inches by 3 inches, and 12 inches by 2 inches.
To find the possible dimensions of the part of the canvas that Ariana will paint yellow, we need to subtract the area she will paint blue from the total area of the canvas.
Given that the total area of the canvas is 36 square inches and the area she will paint blue is 3 inches by 4 inches, we can calculate the area of the blue part:
Area of blue part = length × width = 3 inches × 4 inches = 12 square inches
To find the area of the yellow part, we subtract the area of the blue part from the total area of the canvas:
Area of yellow part = Total area of the canvas - Area of blue part = 36 square inches - 12 square inches = 24 square inches
Now we need to find the possible dimensions that can give us an area of 24 square inches. The dimensions can be any two numbers that multiply together to give 24. Some possible dimensions are:
- 2 inches by 12 inches (2 inches × 12 inches = 24 square inches)
- 3 inches by 8 inches (3 inches × 8 inches = 24 square inches)
- 4 inches by 6 inches (4 inches × 6 inches = 24 square inches)
Therefore, the possible dimensions of the part of the canvas that Ariana will paint yellow are 2 inches by 12 inches, 3 inches by 8 inches, and 4 inches by 6 inches.