Suppose the length of each card in the Example is shortened to yard. Will the
area of each card now be greater than or less than square yard? Explain.

Ask by Newton Bright. in the United States

Jan 16,2025

Question

Suppose the length of each card in the Example is shortened to $$ \frac{1}{4} $$ yard. Will the area of each card now be greater than or less than $$ \frac{1}{16} $$ square yard? Explain.

UpStudy AI · Accepted Answer

When the length of each card is shortened to $$ \frac{1}{4} $$ yard, we need to consider how this affects the area of the card.

**Assumption:** Let's assume that the card is rectangular and that both its length and width are being scaled down by the same factor. This is a common scenario when scaling dimensions proportionally.

1. **Original Dimensions:**
   - Let the original length be $$ L $$ yards.
   - Let the original width be $$ W $$ yards.
   - Original area $$ A_{	ext{original}} = L 	imes W $$.

2. **Scaled Dimensions:**
   - New length $$ L_{	ext{new}} = \frac{1}{4}L $$.
   - New width $$ W_{	ext{new}} = \frac{1}{4}W $$.
   - New area $$ A_{	ext{new}} = L_{	ext{new}} 	imes W_{	ext{new}} = \left(\frac{1}{4}Light) 	imes \left(\frac{1}{4}Wight) = \frac{1}{16}LW $$.

3. **Comparison:**
   - The new area $$ A_{	ext{new}} = \frac{1}{16}LW $$.
   - If the original area $$ A_{	ext{original}} = LW $$, then $$ A_{	ext{new}} = \frac{1}{16}A_{	ext{original}} $$.

Therefore, **the area of each card after shortening the length to $$ \frac{1}{4} $$ yard is exactly $$ \frac{1}{16} $$ square yard**. This means the new area is **equal to** $$ \frac{1}{16} $$ square yard, neither greater nor less than this value.

**Conclusion:** The area of each card becomes exactly $$ \frac{1}{16} $$ square yard after shortening the length to $$ \frac{1}{4} $$ yard.

**Answer:**  
After shortening, each card’s area becomes exactly 1⁄16 square yard. Thus, the area is equal to 1/16 sq yd.
After shortening the length to $$ \frac{1}{4} $$ yard, each card's area becomes exactly $$ \frac{1}{16} $$ square yard.

Suppose the length of each card in the Example is shortened to yard. Will the
area of each card now be greater than or less than square yard? Explain.

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Suppose the length of each card in the Example is shortened to yard. Will the area of each card now be greater than or less than square yard? Explain.