Advertisements
Advertisements
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.
Advertisements
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.
APPEARS IN
संबंधित प्रश्न
Name the quadrilaterals whose diagonals are perpendicular bisectors of each other
The following figure is parallelogram. Find the degree values of the unknowns x, y, z.
The following figure is parallelogram. Find the degree values of the unknown x, y, z.
The sum of two opposite angles of a parallelogram is 130°. Find all the angles of the parallelogram.
Find the angles marked with a question mark shown in Fig. 17.27
Construct a rhombus whose diagonals are of length 10 cm and 6 cm.
One side of a rhombus is of length 4 cm and the length of an altitude is 3.2 cm. Draw the rhombus.
Show that each diagonal of a rhombus bisects the angle through which it passes.
State with reason whether the following statement is ‘true’ or ‘false’.
Every rhombus is a rectangle.
Diagonals PR and QS of a rhombus PQRS are 20 cm and 48 cm respectively. Find the length of side PQ.
