QQuestionMathematics
QuestionMathematics
Draw three different arrays that you could make with 36 square inch tiles. Label the side lengths on each of your arrays. Write multiplication sentences for each array to prove that the area of each array is 36 square inches.
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Step 1:I'll solve this problem step by step, following the specified LaTeX formatting guidelines:
Step 2:: Understand the Problem Requirements
- We need to create three different rectangular arrays using 36 square inch tiles - Each array must have different dimensions - The area of each array must be 36 square inches - We'll label the side lengths and write multiplication sentences
Step 3:: First Array - 1 × 36
- Multiplication sentence: $$1 \times 36 = 36
- Length = 1 inch - Width = 36 inches - Visual representation: A long, narrow rectangle
Step 4:: Second Array - 2 × 18
- Multiplication sentence: $$2 \times 18 = 36
- Length = 2 inches - Width = 18 inches - Visual representation: A wider, shorter rectangle
Step 5:: Third Array - 3 × 12
- Multiplication sentence: $$3 \times 12 = 36
- Length = 3 inches - Width = 12 inches - Visual representation: A more square-like rectangle
Step 6:: Verification
- Each array uses exactly 36 square inch tiles - Each multiplication sentence confirms the total area is 36 square inches - The arrays have different dimensions, satisfying the problem requirements
Final Answer
Three arrays with 36 square inch tiles: 1. 1 × 36 inches 2. 2 × 18 inches 3. 3 × 12 inches Each array satisfies the condition of having an area of 36 \text{ square inches} through its unique multiplication sentence.
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