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प्रश्न
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.
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उत्तर
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.
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संबंधित प्रश्न
Given below is a parallelogram ABCD. Complete each statement along with the definition or property used.
(i) AD =
(ii) ∠DCB =
(iii) OC =
(iv) ∠DAB + ∠CDA =
If an angle of a parallelogram is two-third of its adjacent angle, find the angles of the parallelogram.
Two adjacent angles of a parallelogram are as 1 : 2. Find the measures of all the angles of the parallelogram.
Which of the following statement is true for a rhombus?
Its diagonals bisect each other at right angles.
If the diagonals of a rhombus are 12 cm and 16cm, find the length of each side.
Diagonals of a rhombus are 20 cm and 21 cm respectively, then find the side of rhombus and its perimeter.
If the adjacent sides of a parallelogram are equal then parallelogram is a ______.
If all sides of a quadrilateral are equal, it is a ______.
Diagonals of a quadrilateral are perpendicular to each other. Is such a quadrilateral always a rhombus? Give a figure to justify your answer.
Construct a rhombus whose side is 5 cm and one angle is of 60°.
