Question

ABCD is a rectangle inscribed in a semicircle if length and breadth of the rectangle are in the ratio 2 is to 1 what is the ratio of perimeter of rectangle and diameter of semicircle

Answer 1

refer diagram...
from the diagram
a²+a²=r²
a/r=√2
4a/2r=2√2

Answer 2

The ratio of the perimeter of the rectangle and the diameter of the semicircle will be 3 : √2

Step-by-step explanation:

Let the length of the rectangle is 2x and the breadth is x.

And the radius of the semicircle is assumed to be r.

Now, see the diagram attached.

From, Δ OAB, OA = x and AB = x and OB = r and ∠ OAB = 90°.

So, applying Pythagoras Theorem r² = x² + x²

⇒ r = √2x.

Now, perimeter of the rectangle is 2(2x + x) = 6x

And the diameter of the semicircle is 2r = 2√2x

Hence, the ratio of the perimeter of the rectangle and the diameter of the semicircle will be 6x : 2√2x = 3 : √2 (Answer)