Question

1. higher order thinking george has a 1 sheet of paper. he cuts it into 6 inches by 5 inches, and 3 inches by 6 inches. what were the dimensions and total area of his original sheet of paper? explain

Explanation:

Step1: Analyze the problem

We know that after cutting the paper into 6 pieces of 5 inches by 3 inches by 6 inches (assuming it's a rectangular prism or a rectangle, maybe a typo and it's a rectangle, so area), we need to find the original area. Wait, maybe it's a sheet of paper, so area. Each piece has dimensions, let's assume it's a rectangle, so area of each piece is length * width. Wait, the problem says "cuts it into 6 inches by 5 inches, and 3 inches by 6 inches"? Wait, maybe the original sheet is cut into 6 pieces, each with area (let's correct the problem: maybe each piece is 5 inches by 3 inches? Wait, the text is a bit garbled. Wait, re-reading: "He cuts it into 6 inches by 5 inches, and 3 inches by 6 inches. What were the dimensions and total of his original sheet of paper? EXF" Wait, maybe it's that he cuts the original sheet into 6 pieces, each with area (5*3) or (3*6)? No, maybe the original sheet is cut into pieces, and we need to find the original dimensions. Wait, maybe the correct problem is: A sheet of paper is cut into 6 pieces, each of size 5 inches by 3 inches. Wait, no, the text says "cuts it into 6 inches by 5 inches, and 3 inches by 6 inches" – maybe it's a mistake, and it's 6 pieces, each with area (5*3) or (3*6)? Wait, maybe the original sheet's area is the sum of the areas of the 6 pieces. Wait, let's assume that he cuts the sheet into 6 pieces, each with dimensions 5 inches by 3 inches. Wait, no, the text is: "He cuts it into 6 inches by 5 inches, and 3 inches by 6 inches. What were the dimensions and total of his original sheet of paper? EXF" – maybe it's a typo, and it's 6 pieces, each of size 5 inches by 3 inches, and 3 inches by 6 inches? No, maybe the original sheet is a rectangle, and when cut, the pieces have areas, and we need to find the original area. Wait, maybe the correct problem is: A sheet of paper is cut into 6 pieces, each with dimensions 5 in × 3 in. What is the area of the original sheet? Wait, no, the user's text is: "7. Higher Order Thinking Geroge has a sheet of paper. He cuts it into 6 inches by 5 inches, and 3 inches by 6 inches. What were the dimensions and total of his original sheet of paper? EXF" Wait, maybe it's that he cuts the original sheet into two types of pieces? No, maybe it's a mistake, and it's 6 pieces, each with area (5*6) or (3*6)? Wait, maybe the original sheet's area is the sum of the areas of all pieces. Wait, let's assume that he cuts the sheet into 6 pieces, each with dimensions 5 in × 3 in. Then total area is 6*(5*3). But the text says "6 inches by 5 inches, and 3 inches by 6 inches" – maybe it's a single piece? No, the problem is unclear, but let's assume that the original sheet is cut into 6 pieces, each with area (5*3) = 15 square inches, so total area is 6*15 = 90. But maybe the dimensions are such that length and width are multiples. Wait, maybe the correct problem is: George has a sheet of paper. He cuts it into 6 pieces, each of size 5 inches by 3 inches. What is the area of the original sheet? Then total area is 6*(5*3) = 90. But the text is garbled. Alternatively, maybe the original sheet is cut into pieces with dimensions 6x5 and 3x6, but that doesn't make sense. Wait, maybe the problem is: A sheet of paper is cut into 6 pieces, each with length 5 inches and width 3 inches. Find the area of the original sheet. Then:

Step1: Calculate area of one piece

Area of one piece = length * width = $5 \times 3 = 15$ square inches.

Step2: Calculate total area of original sheet

Since there are 6 pieces, total area = $6 \times 15 = 90$ square inches.

Now, for dimensions, we need to find length and width such that length * width = 90. Possible dimensions: 9x10, 15x6, 18x5, 30x3, 45x2, 90x1. But maybe the pieces are arranged, so if each piece is 5x3, then the original sheet could be (5*3) x (3*2) = 15x6, since 5*3=15 and 3*2=6, and 15*6=90, and 15/5=3, 6/3=2, so 3*2=6 pieces. Yes, that makes sense. So original dimensions are 15 inches by 6 inches, total area 90 square inches.

Answer:

Original dimensions: 15 inches by 6 inches, Total area: 90 square inches