Given $$ \sqrt{49}=7 $$, which of the following statements is true? $$ 49^{2}=7 $$ 7 is the length of a side of a square with an area of 49 . 7 is the length of a side of a square with a perimeter $$ =49 $$. $$ \sqrt{7}=49 $$

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UpStudy AI · Accepted Answer

Let's analyze each statement one by one based on the known condition $$ \sqrt{49} = 7 $$.

1. **Statement: $$ 49^{2} = 7 $$**  
   This statement is false because $$ 49^{2} = 2401 $$, not 7.

2. **Statement: 7 is the length of a side of a square with an area of 49.**  
   The area $$ A $$ of a square is given by $$ A = s^2 $$, where $$ s $$ is the length of a side.  
   If the area is 49, then:  
   $$
   s^2 = 49 \implies s = \sqrt{49} = 7
   $$  
   This statement is true.

3. **Statement: 7 is the length of a side of a square with a perimeter $$ = 49 $$.**  
   The perimeter $$ P $$ of a square is given by $$ P = 4s $$.  
   If the perimeter is 49, then:  
   $$
   4s = 49 \implies s = \frac{49}{4} = 12.25
   $$  
   This statement is false.

4. **Statement: $$ \sqrt{7} = 49 $$**  
   This statement is false because $$ \sqrt{7} $$ is approximately 2.6457513110645906, not 49.

Based on the analysis, the only true statement is:

**7 is the length of a side of a square with an area of 49.**
7 is the length of a side of a square with an area of 49.

Given \( \sqrt{49}=7 \), which of the following statements is true? \( 49^{2}=7 \) 7 is the length of a side of a square with an area of 49 . 7 is the length of a side of a square with a perimeter \( =49 \). \( \sqrt{7}=49 \)

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