Lee wants to cut this piece of canvas into two rectangles that are 3×2 and 3×5. He wants the sum of the two small recyangles to be the same as the area of the large rectangle. Can he do this? Explain the rectangle is 6feet across and 3feet tall
3x2 + 3x5 = 6+15 = 21
8x3 = 18
So, he needs more canvas than he has.
Or, you could line up the two desired pieces, and he needs one large piece 3x(2+5) = 3x7, but his piece is only 3x6.
To determine whether Lee can cut the canvas into two rectangles with dimensions 3×2 and 3×5, we need to compare the sum of the areas of the small rectangles to the area of the large rectangle.
The area of a rectangle is calculated by multiplying its length by its width. In this case, the large rectangle has a length of 6 feet and a width of 3 feet, so its area is 6 × 3 = 18 square feet.
Now, let's calculate the area of the two small rectangles. The first rectangle has dimensions 3×2, so its area is 3 × 2 = 6 square feet. The second rectangle has dimensions 3×5, so its area is 3 × 5 = 15 square feet.
To find the sum of the areas of the two small rectangles, we add their individual areas together: 6 + 15 = 21 square feet.
Since the sum of the areas of the two small rectangles (21 square feet) is greater than the area of the large rectangle (18 square feet), it is not possible for Lee to cut the canvas into two rectangles with the given dimensions while having the sum of their areas equal to the area of the large rectangle.
In summary, Lee cannot cut the canvas into two rectangles with dimensions 3×2 and 3×5, where the sum of their areas equals the area of the large rectangle (6 feet by 3 feet).