Correct Answer – Option 3 : 130 cm

Given – 

area of rectangle = 812 cm², area of semicircle = 98π cm²

Formula used – 

area of rectangle = length × breadth

area of semicircle = (1/2) × π × radius²

Solution – 

Let the radius of the semi – circle is r cm.

⇒ (1/2) × π r² = 98π  

⇒ r² = 196

⇒ r = 14 cm

⇒ diameter of the semi – circle = 28 cm

⇒ diameter of semi – circle = side of rectangle CD = 28 cm

⇒ area of rectangle = 812 cm²

⇒ BC × CD = 812

⇒ BC × 28 = 812

⇒ BC = 29 cm

⇒ We have to find perimeter of remaining figure so,

⇒ perimeter = AB + BC + AD + (1/2) × perimeter of the circle

⇒ perimeter = 28 + 29 + 29 + (1/2) × (2πr)

⇒ perimeter = 58 + 28 + (22/7) × 14

⇒ perimeter = 130 cm

∴ perimeter of remaining figure = 130 cm.