Let's analyze Justine's expression for the perimeter of the rectangular playground, which is modeled as \( 5w + 5w + w + w \).
First, we simplify this expression:
\[ 5w + 5w + w + w = 10w + 2w = 12w \]
Now, we can check each of the statements to see which ones are correct based on this simplification:
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The expression 12w shows the perimeter is 12 times the width.
- True. This statement correctly describes the simplified expression.
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The expression 2(5w)+2w shows the length is 5 times the width.
- The expression \(2(5w) + 2w\) simplifies to \(10w + 2w = 12w\). This indicates that \(h = 2w\) (height is twice the width) if we assume \(l = 5w\) (length is five times the width) is part of the overall context. True, this does imply the width is being referenced correctly.
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The expression 10w + 2w shows the length is 10 times the width.
- The expression simplifies to \(12w\), not indicating that the length is 10 times the width. False.
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The expression 5(w + w + w + w) shows the perimeter is 5 times the width.
- The expression \(5(w + w + w + w)\) simplifies to \(5 \times 4w = 20w\), which does not reflect Justine's original perimeter of \(12w\). False.
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The expression 10 + w shows the perimeter is 10 plus the width.
- The expression incorrectly denotes that it refers to a perimeter; it simplifies to \(10 + w\), which has nothing to do with the overall perimeter of the playground. False.
Correct Answers:
- The expression 12w shows the perimeter is 12 times the width.
- The expression 2(5w) + 2w shows the length is 5 times the width.
3 answers