Question
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.
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 = 3 units.
We know that, diagonals of the rhombus bisect each other at 90∘.
Now,
In ΔOAB,(AB)2=(OA)2+(OB)2 [by Pythagoras theorem]
⇒(AB)2=(4)2+(3)2=25⇒AB=√25⇒AB=5units
Since, AB is diameter of semi-circle.
∴ Radius =Diameter2=AB2=52=2.5units
Hence, radius of semi-circle is 2.5 units.
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:
In rhombus ABCD,
AO = OP + PA = 2 + 2 = 4 units and OB = OQ+QB = 2 + 1 = 3 units.
We know that, diagonals of the rhombus bisect each other at 90∘.
Now,
In ΔOAB,(AB)2=(OA)2+(OB)2 [by Pythagoras theorem]
⇒(AB)2=(4)2+(3)2=25⇒AB=√25⇒AB=5units
Since, AB is diameter of semi-circle.
∴ Radius =Diameter2=AB2=52=2.5units
Hence, radius of semi-circle is 2.5 units.
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