The perimeter of a rectangle is $108 ext{ cm}$ and its length is $40 ext{ cm}$. How many semicircles of the maximum possible radius can be drawn inside the rectangle?

Question

The perimeter of a rectangle is $108 	ext{ cm}$ and its length is $40 	ext{ cm}$. How many semicircles of the maximum possible radius can be drawn inside the rectangle?

Accepted Answer

**Solution:**

1. Let the length and breadth of the rectangle be $l$ cm and $b$ cm respectively.

2. Given the perimeter $P = 2(l + b) = 108$ cm.

3. Substitute $l = 40$ cm:
   $$2(40 + b) = 108 \ 40 + b = 54 \ b = 14 	ext{ cm}$$

4. The maximum radius of a semicircle that can fit inside the rectangle depends on the smaller dimension, which is the breadth $b = 14$ cm.

5. However, the question asks for the number of semicircles of maximum radius that can be drawn inside the rectangle, but it does not specify how these semicircles are arranged or their orientation.

6. Without information about the arrangement or spacing of semicircles inside the rectangle, it is impossible to determine the exact number of semicircles that can fit.

**Answer:** Cannot be determined

Answer

Answer

Answer