Question

A Rangoli has been drawn on a flor of a house. ABCD and PQRS both are in the shape of a rhombus. Find the radius of semicircle drawn on each side of rhombus ABCD.

Answer 1

In rhombus ABCD,

AO = OP + PA

= 2 + 2

= 4 units

And OB = OQ + QB

= 2 + 1

= 3 units

We know that, diagonals of rhombus bisect each other at 90°.

Now, In ΔOAB,

(AB)² = (OA)² + (OB)²  ...[By Pythagoras theorem]

⇒ (AB)² = (4)² + (3)²

⇒ (AB)² = 16 + 9

⇒ (AB)² = 25

⇒ AB = `sqrt(25)`

⇒ AB = 5 units

Since, AB is diameter of semi-circle.

∴ Radius = `"Diameter"/2`

= `(AB)/2`

= `5/2`

= 2.5 units

Hence, radius of the semi-circle is 2.5 units.