The area, perimeter and diagonals of a square area a, b, c respectively. Then the value of `(bc)/(a)` is.

Options

A. A)4
B. B)2
C. C)`4sqrt(2)`
D. D)`2sqrt(2)`

Answer

To solve the problem, we need to find the value of \(\frac{bc}{a}\) where \(a\) is the area, \(b\) is the perimeter, and \(c\) is the diagonal of a square.

### Step-by-Step Solution:

1. **Identify the side of the square**:
Let's denote the side length of the square as \(s\).

2. **Calculate the area \(a\)**:
The area of a square is given by the formula:
\[ a = s^2 \]

3. **Calculate the perimeter \(b\)**:
The perimeter of a square is given by the formula:
\[ b = 4s \]

4. **Calculate the diagonal \(c\)**:
The length of the diagonal of a square can be calculated using the Pythagorean theorem:
\[ c = s\sqrt{2} \]

5. **Substitute the values into \(\frac{bc}{a}\)**:
Now we substitute the values of \(b\), \(c\), and \(a\) into the expression:
\[ \frac{bc}{a} = \frac{(4s)(s\sqrt{2})}{s^2} \]

6. **Simplify the expression**:
Simplifying the expression:
\[ \frac{bc}{a} = \frac{4s^2\sqrt{2}}{s^2} \]
The \(s^2\) in the numerator and denominator cancels out:
\[ \frac{bc}{a} = 4\sqrt{2} \]

### Final Answer:
Thus, the value of \(\frac{bc}{a}\) is \(4\sqrt{2}\).

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