Final answer:
The students should paint a red square with an area that is 1/5 of the entire canvas. The area of the canvas is 100 square inches, so the red square should be approximately 20 square inches. The side length of the red square, calculated for practicality in a classroom, should be 4 inches.
Step-by-step explanation:
The art teacher gave each student a 10 inch x 10 inch canvas and instructed them to paint a red square on 1/5 of the canvas.
To find the size of the red square, we start by calculating the area of the canvas, which is 10 inches x 10 inches, resulting in 100 square inches.
Since the red square should cover 1/5 of the canvas, we divide the total area by 5. This gives us 100 / 5 = 20 square inches for the area of the red square.
To determine the side length of the square, we take the square root of the area. The square root of 20 is approximately 4.47 inches, but since we're dealing with a square whose sides are whole numbers, we'll round the side length down to 4 inches for practicality in a classroom setting.
Therefore, the red square each student should paint will be 4 inches x 4 inches.
Remember, it's important to acknowledge that the exact side length is approximately 4.47 inches, however, for the purposes of simplicity and the materials possibly used in a classroom situation, the 4 inch x 4 inch size is a suitable approximation that is close to the precise calculation.