Question

Rafael wants to paint a rectangular region of a wall with one layer of paint. He has 28 yards of tape to tape around the border of the region he paints. He is considering three regions with lengths of 5 yards, 6 yards, and 7 yards. Answer the questions below to find which of these regions would require the most paint.

Answer 1

To find the region that requires the most paint, compare the areas of the three rectangular regions. Calculate the areas by multiplying the length and width of each region. Then, find the dimensions of the regions that use up all of the 28 yards of tape and determine the region with the largest area.

Step-by-step explanation:

To find which of the three regions would require the most paint, we need to compare the areas of the three rectangular regions. The area of a rectangle can be found by multiplying its length by its width. Let's calculate the areas of the three regions and compare them:

1. Region A: Length = 5 yards, Width = Unknown (let's call it x)
   Area = 5x square yards
2. Region B: Length = 6 yards, Width = Unknown (let's call it y)
   Area = 6y square yards
3. Region C: Length = 7 yards, Width = Unknown (let's call it z)
   Area = 7z square yards

Now, we need to find the dimensions of the regions that would use up all of the 28 yards of tape. Each side of the rectangles will have tape on both ends, so we need to subtract twice the tape length from the total length of the region. Therefore, we have the following equations:

1. 2(x + 5) = 28
2. 2(y + 6) = 28
3. 2(z + 7) = 28

By solving these equations, we can find the values of x, y, and z. Once we have the values of x, y, and z, we can calculate the areas of the regions and determine which one requires the most paint.