Advertisements
Advertisements
Question
Diagonals of a rhombus are 20 cm and 21 cm respectively, then find the side of rhombus and its perimeter.
Advertisements
Solution
Let `square`ABCD be the rhombus.
AC = 20 cm, BD = 21 cm
AO = `1/2` AC ...[Diagonals of a rhombus bisect each other]
= `1/2 xx 20`
= 10 cm ...(i)
BO = `1/2` BD ...[Diagonals of a rhombus bisect each other]
= `1/2 xx21`
= `21/2`
= 10.5 cm ...(ii)
In ∆AOB,
∠AOB = 90° ...[Diagonals of a rhombus are perpendicular to each other]
By Pythagoras theorem,
∴ AB2 = AO2 + BO2
∴ AB2 = 102 + 10.52
∴ AB2 = 100 + 110.25
∴ AB2 = 210.25
∴ AB = `sqrt(210.25)`
∴ AB = 14.5 cm
Perimeter of `square`ABCD = 4 × AB
= 4 × 14.5
= 58 cm
APPEARS IN
RELATED QUESTIONS
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 =
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.
Two adjacent angles of a parallelogram are as 1 : 2. Find the measures of all the angles of the parallelogram.
ABCD is a parallelogram in which ∠A = 70°. Compute ∠B, ∠C and ∠D.
In a parallelogram ABCD, AB = 10 cm, AD = 6 cm. The bisector of ∠A meets DC in E, AEand BC produced meet at F. Find te length CF.
Fill in the blank, inthe following, so as to make the statement true:
A square is a rhombus in which .....
Fill in the blank, inthe following, so as to make the statement true:
A rhombus has all its sides of ...... length.
The diagonals of a parallelogram are not perpendicular. Is it a rhombus? Why or why not?
If the diagonals of a rhombus are 12 cm and 16cm, find the length of each side.
Construct a rhombus whose diagonals are of length 10 cm and 6 cm.
Draw a rhombus, having each side of length 3.5 cm and one of the angles as 40°.
One side of a rhombus is of length 4 cm and the length of an altitude is 3.2 cm. Draw the rhombus.
Draw a rhombus ABCD, if AB = 6 cm and AC = 5 cm.
ABCD is a rhombus and its diagonals intersect at O.
(i) Is ∆BOC ≅ ∆DOC? State the congruence condition used?
(ii) Also state, if ∠BCO = ∠DCO.
If all pairs of adjacent sides of a quadrilateral are congruent then it is called ______.
The lengths of the diagonals of a Rhombus are 12 cm and 16 cm. Find the side of the rhombus
In the figure, BEST is a rhombus, Then the value of y – x is ______.
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°.
