Explanation:

Let's solve step-by-step:

- Let radius of circle = r, Breadth of rectangle = b, Length = 36 cm

- Area of circle = pr² = (22/7)r²

- Area of rectangle = 36 × b

- Ratio of areas = [(22/7)r²] / (36b) = 77/18

- Cross-multiplied: (22/7)r² × 18 = 77 × 36b

- (22 × 18)r² / 7 = 77 × 36b

- 396r² / 7 = 2772b

- 396r² = 19404b

- r² = 19404b / 396

- r² = 49b

Given: Breadth : Radius = 2 : 7 ? b / r = 2 / 7 ? r = (7/2) b

- From previous: r² = 49b

- Substitute r: (7b/2)² = 49b

- (49b²)/4 = 49b

- (49b²)/4 = 49b

- b² = 4b

- b = 4 (since b ? 0)

Now,

- r = (7/2) × 4 = 14 cm

- Diameter = 2r = 28 cm

- Product of diameter & breadth = 28 × 4 = 112 cm

Options:

1. 142 cm

2. 112 cm 

3. 124 cm

4. 144 cm

5. 104 cm

The correct answer is Option 2 – 112 cm.