Institution: Bangladesh Bank Exam: Officer (Cash) -Sonali Bank | BD Development | BD Krishi Bank - 12.10.2018 ||
Topic: Mathematics (সাধারণ গণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

To solve the problem, we need to use the given information about the perimeter and area of the rectangle. Let the length of the rectangle be \( L \) and the width be \( W \).

The perimeter \( P \) of a rectangle is given by the formula:
\[
P = 2(L + W)
\]
Setting this equal to the provided perimeter, we have:
\[
2(L + W) = 76
\]
Dividing both sides by 2 gives us:
\[
L + W = 38 \quad (1)
\]

The area \( A \) of a rectangle is given by:
\[
A = L \times W
\]
Setting this equal to the given area, we have:
\[
L \times W = 360 \quad (2)
\]

From equation (1), we can express \( W \) in terms of \( L \):
\[
W = 38 - L
\]
Substituting this expression for \( W \) into equation (2) gives:
\[
L(38 - L) = 360
\]
Expanding this, we get:
\[
38L - L^2 = 360
\]
Rearranging leads to the quadratic equation:
\[
L^2 - 38L + 360 = 0
\]

To solve this quadratic equation, we can use the quadratic formula \( L = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \):
\[
L = \frac{38 \pm \sqrt{(-38)^2 - 4 \cdot 1 \cdot 360}}{2 \cdot 1}
\]
Calculating the discriminant:
\[
b^2 - 4ac = 1444 - 1440 = 4
\]
Thus:
\[
L = \frac{38 \pm 2}{2}
\]
This gives us two potential solutions for \( L \):
\[
L = 20 \quad \text{or} \quad L = 18
\]

Using \( L + W = 38 \) we find corresponding widths:
- If \( L = 20\): \( W = 38 - 20 = 18 \)
- If \( L = 18\): \( W = 38 - 18 = 20 \)

In both cases, one side is \( 18 \) and the other \( 20 \). The shortest side is therefore \( 18 \), which matches option C. This demonstrates that option C is correct.