The circumference of the semicircle is 54cm. If the side of square is 40% more than the diameter of the semicircle, then what is the perimeter of the square?Choices:- 132.6cm 111.6cm 154.6cm 117.6cm

Step 1: Find the diameter of the semicircle

The formula for the circumference of a circle is C = πd. Since we have a semicircle, the circumference will be half of that of a full circle plus the diameter (which is the straight line across the semicircle). So, we have:

C = 1/2 * πd + d

Given that the circumference of the semicircle is 54 cm, we can set up the equation:

54 = 1/2 * πd + d

Step 2: Solve for d

To solve for d, we first combine like terms:

54 = d(1/2π + 1)

Then, divide both sides by (1/2π + 1) to isolate d:

d = 54 / (1/2π + 1)

Solving this gives us approximately d = 21.9911 cm.

Step 3: Find the side of the square

The problem states that the side of the square is 40% more than the diameter of the semicircle. So, we calculate:

Side of square = d + 0.40d = 21.9911 cm + 0.40 * 21.9911 cm = 30.7875 cm

Step 4: Find the perimeter of the square

The perimeter of a square is simply four times the length of one side. So, we calculate:

Perimeter of square = 4 * side of square = 4 * 30.7875 cm = 123.15 cm

So, the perimeter of the square is approximately 123.15 cm. The closest choice to this is 132.6 cm.