Advertisements
Advertisements
प्रश्न
Diagonals of a rhombus are 20 cm and 21 cm respectively, then find the side of rhombus and its perimeter.
Advertisements
उत्तर
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
संबंधित प्रश्न
Name the quadrilaterals whose diagonals are perpendicular bisectors of each other
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 =
In the following figure GUNS and RUNS are parallelogram. Find x and y.
The measure of one angle of a parallelogram is 70°. What are the measures of the remaining angles?
Two adjacent angles of a parallelogram are as 1 : 2. Find the measures of all the angles of the parallelogram.
The sum of two opposite angles of a parallelogram is 130°. Find all the angles of the parallelogram.
In the following Figure ABCD is a arallelogram, CE bisects ∠C and AF bisects ∠A. In each of the following, if the statement is true, give a reason for the same:
(i) ∠A = ∠C
(ii) \[\angle FAB = \frac{1}{2}\angle A\]
(iii) \[\angle DCE = \frac{1}{2}\angle C\]
(iv) \[\angle CEB = \angle FAB\]
(v) CE || AF
Which of the following statement is true for a rhombus?
It has two pairs of equal sides.
Which of the following statement is true for a rhombus?
It is a parallelogram.
Which of the following statement is true for a rhombus?
It is a quadrilateral.
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.
Show that each diagonal of a rhombus bisects the angle through which it passes.
Which of the following statement is true for a rectangle?
Its diagonals are equal and bisect each other.
State with reason whether the following statement is ‘true’ or ‘false’.
Every parallelogram is a rhombus.
Lengths of diagonals of a rhombus ABCD are 16 cm and 12 cm. Find the side and perimeter of the rhombus.
If all sides of a quadrilateral are equal, it is a ______.
A rhombus is a parallelogram in which ______ sides are equal.
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 CLUE in which CL = 7.5 cm and LE = 6 cm.
