1.

A rangoli has been drawn on the floor of a house. ABCD and PQRS both are in the shape of a rhombus. Find the radius of semi-circle drawn on each side of rhombus ABCD.

Answer»

In Rhombus ABCD,

AO = OP + PA = 2+2 = 4 units.

And, OB = OQ + QB = 2 + 1 = 2 units.

Now,

We know that the diagonals of the rhombus bisect at 900

∴ In ΔOAB,

AB2 = OA2 + OB2

⇒ AB2 = 42 + 32

⇒ AB = √25

⇒ AB = 5 units.

Now, AB is also the diameter of the semi-circle.

∴ radius of the circle will be 2.5 units.



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