In the given figure, A B C D is a rectangle inscribed in a semi-circle. If the length and the breadth of the rectangle are in the ratio 2: 1. What is the ratio of the perimeter of the rectangle to the diameter of the semicircle?

Question

In the given figure, A B C D is a rectangle inscribed in a semi-circle. If the length and the breadth of the rectangle are in the ratio 2: 1. What is the ratio of the perimeter of the rectangle to the diameter of the semicircle? (A) 3: √2 (B) 2: √3 (C) 2: √5 (D) 3: √5

Tardigrade Admin · Accepted Answer

(i) Join O C and find the relation between O B and BC. (ii) O B=B C and O C: O B=√2: 1.

Q. In the given figure, $A BC D$ is a rectangle inscribed in a semi-circle. If the length and the breadth of the rectangle are in the ratio $2 : 1$ . What is the ratio of the perimeter of the rectangle to the diameter of the semicircle?

$3 : 2$

$2 : 3$

$2 : 5$

$3 : 5$

(i) Join $OC$ and find the relation between $OB$ and BC.
(ii) $OB = BC$ and $OC : OB = 2 : 1$ .

Q. In the given figure, ABCD is a rectangle inscribed in a semi-circle. If the length and the breadth of the rectangle are in the ratio 2:1. What is the ratio of the perimeter of the rectangle to the diameter of the semicircle?

3:2​

2:3​

2:5​

3:5​