The diagonal of a square is 10 cm. What will be the length of the diagonal of the square whose area is double of the area of first square?

Options

A. a) `10sqrt2 cm`
B. b) `8sqrt2 cm`
C. c) `20sqrt2 cm`
D. d) `20 cm`

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Find the side length of the first square
Given that the diagonal of the first square is 10 cm, we can use the relationship between the side length (A) of a square and its diagonal (D):
\[ D = A \sqrt{2} \]
Substituting the value of the diagonal:
\[ 10 = A \sqrt{2} \]
To find A, we rearrange the equation:
\[ A = \frac{10}{\sqrt{2}} \]

### Step 2: Calculate the area of the first square
The area (Area1) of a square is given by:
\[ \text{Area} = A^2 \]
Substituting the value of A we found:
\[ \text{Area1} = \left(\frac{10}{\sqrt{2}}\right)^2 \]
Calculating this gives:
\[ \text{Area1} = \frac{100}{2} = 50 \text{ cm}^2 \]

### Step 3: Find the area of the second square
According to the problem, the area of the second square is double that of the first square:
\[ \text{Area2} = 2 \times \text{Area1} = 2 \times 50 = 100 \text{ cm}^2 \]

### Step 4: Find the side length of the second square
Using the area of the second square, we can find its side length (B):
\[ \text{Area2} = B^2 \]
Thus:
\[ 100 = B^2 \]
Taking the square root of both sides:
\[ B = 10 \text{ cm} \]

### Step 5: Calculate the diagonal of the second square
Now we can find the diagonal (D2) of the second square using the same relationship:
\[ D2 = B \sqrt{2} \]
Substituting the value of B:
\[ D2 = 10 \sqrt{2} \text{ cm} \]

### Conclusion
The length of the diagonal of the square whose area is double that of the first square is:
\[ \boxed{10 \sqrt{2} \text{ cm}} \]

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