Question

The area of the circle is 154 cm² and the perimeter of the rectangle is 128.56% of the diameter of the circle then what is the value of the diagonal of the rectangle if the length of the rectangle is 4 cm?
1. √51
2. √41
3. √31
4. √43
5. None

Answer 1

Correct Answer - Option 2 : √41

Calculation:

Let be assume the radius of the circle is R

⇒ π × R² = 154, R = 7 cm

⇒ Diameter of circle = 2 × 7 = 14 cm

We know, 128.56% = 1 + 2/7 in fraction form

⇒ The perimeter of rectangle = 14 × (1 + 2/7) = 18 cm

⇒ 2 × (4 + b) = 18  where b = Breadth of the rectangle 

⇒ b = 5

⇒ The diagonal of rectangle = √(5² + 4²) = √41

∴ The required result will be √41.