Lee wants to cut this piece of canvas into two rectangles that are 3 x 2 and 3 x 5. He wants the sum of the areas of the two small rectangles to be the same as the area of the large rectangle. Can he do this? explain.
Yes.
If the original piece of canvas is 3 x 7.
3*7 = 21 square units
3*2 = 6
3*5 = 15
6+15 = 21
I got that he can do it my explaining is that he could he can't do this.
To determine if Lee can cut the canvas into two rectangles with the specified dimensions and equal sum of areas, we need to calculate the area of the large rectangle and compare it to the sum of the areas of the small rectangles.
The dimensions of the large rectangle are not provided in the question, so we have to find them first. To do this, we can use the given dimensions of the small rectangles.
The dimensions of one of the small rectangles are 3 x 2, so its area is calculated by multiplying its length (3) by its width (2), which gives us an area of 6 square units.
The dimensions of the other small rectangle are 3 x 5, so its area is calculated by multiplying its length (3) by its width (5), which gives us an area of 15 square units.
To find the dimensions of the large rectangle, we can add the widths of the two small rectangles together (2 + 5 = 7) and take the maximum of the two lengths of the small rectangles (3). Therefore, the dimensions of the large rectangle are 7 x 3.
To calculate the area of the large rectangle, multiply its length (7) by its width (3), which gives us an area of 21 square units.
Now we can compare the area of the large rectangle (21 square units) with the sum of the areas of the two small rectangles (6 + 15 = 21 square units).
Since the area of the large rectangle and the sum of the areas of the small rectangles are equal (21 = 21), Lee can indeed cut the canvas into two rectangles with the specified dimensions so that the sum of their areas is equal to the area of the large rectangle.