Find the circumference (in m) of the largest circle that can be drawn completely inside a rectangle whose dimensions are given as 14 m and 116 m.

Correct Answer: The correct option is 44 (Option 2).

Step-by-Step Explanation:

1. Understanding the Dimensions:

We are given a rectangle with:

Length = 116 m

Breadth = 14 m

2. Determining the Maximum Circle Size:

The largest circle that can fit completely inside a rectangle is limited by the smaller dimension of the rectangle. If the diameter of the circle were larger than the smaller side (14 m), the circle would extend outside the boundaries of the rectangle.

Therefore, the maximum diameter ($d$) of the circle is equal to the breadth of the rectangle:

$d=14\text{m}$

The radius ($r$) of the circle is half of its diameter:

$r=\frac{d}{2}=\frac{14}{2}=7\text{m}$

3. Calculating the Circumference:

The formula for the circumference ($C$) of a circle is:

$C=2\times \pi \times r$

Using the standard approximation $\pi =\frac{22}{7}$:

$C=2\times \frac{22}{7}\times 7$

Simplifying the calculation by cancelling out 7 from the numerator and denominator:

$C=2\times 22=44\text{m}$

Thus, the circumference of the largest circle that can be drawn inside the rectangle is 44 m.