If two squares X and Y have each side of 10 m and 20 m respectively, then the side of the square Z whose area is equal to the sum of the areas of square X and square Y is:

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Accepted Answer

#### Step 1: Calculate Areas of Squares X and Y
The area of a square is given by:  
$$
	ext{Area} = (	ext{Side})^2
$$

- For square X:  
  $$ 
  	ext{Area of X} = (10)^2 = 100 \, 	ext{m}^2 
  $$

- For square Y:  
  $$ 
  	ext{Area of Y} = (20)^2 = 400 \, 	ext{m}^2 
  $$

#### Step 2: Sum of Areas
The total area (area of square Z) is:  
$$ 
	ext{Area of Z} = 	ext{Area of X} + 	ext{Area of Y} = 100 + 400 = 500 \, 	ext{m}^2 
$$

#### Step 3: Side of Square Z
The side of square Z is found by taking the square root of its area:  
$$ 
	ext{Side of Z} = \sqrt{	ext{Area of Z}} = \sqrt{500}
$$

Simplify further:  
$$ 
\sqrt{500} = \sqrt{100 	imes 5} = 10\sqrt{5}
$$

#### Step 4: Verify with Code
The code confirms that the side length is approximately **22.36 m**, which matches $$ 10\sqrt{5} $$.

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Thus, the side length of square Z is **$$ 10\sqrt{5} \, 	ext{m} $$**, making Option **(d)** correct.

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