The length of the diagonals of a rhombus is 42 cm and 40 cm. Find the perimeter of the rhombus.
Answers
Step-by-step explanation:
Given:-
The length of the diagonals of a rhombus is 42 cm and 40 cm.
To find:-
Find the perimeter of the rhombus.
Solution :-
From the given figure,
ABCD is a rhombus
AC and BD are the two diagonals are interesting to each other at O
AC = 40 cm
BD = 42 cm
We know that
In a rhombus Diagonals are perpendicular bisectors to each other.
AO=OC=AC/2 = 40/2= 20 cm
BO=OD =BD/2 = 42/2 =21 cm
The two signals divides the rhombus into four right angled triangles and they are congruent
∆AOB =∆BOC = ∆COD=∆DOA
from ∆AOB we have AO = 20 cm and OB =21 cm
Since ∆AOB is a right angled triangle
By Pythagoras theorem
AB^2 = AO^2+OB^2
=>AB^2 = (20)^2+(21)^2
=>AB^2 = 400+441
=>AB^2 =841
=>AB=√841
=>AB=29 cm
The value of the side of the rhombus=29 cm
Since all the four sides are equal in a rhombus.
AB=BC=CD=DA=29 cm
Now Perimeter of a rhombus = 4× Length of the side
=>Perimeter = 4×29 cm
=>Perimeter = 4×29 cm
=>Perimeter = 116 cm
Answer:-
Perimeter of the given rhombus ABCD = 116 cm
Used formulae:-
Properties of Rhombus:-
- All four sides are equal.
- Two diagonals are not equal.
- Diagonals are perpendicular bisectors to each other.
- Diagonals divides the rhombus into four congruent right angles.
- Perimeter of a rhombus = 4× length of the side
Pythagoras theorem:-
- In a right angled triangle,the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Answer:
as we know that digonal of a rhombus bisect each other therefore AO =20cm and BO=21cm.
then, use formula AB=√(AO*AO+OB*OB).
then AB=√(20*20+21*21)
AB=√(400+441)
AB=√481
AB=√29*29
AB=29cm.
as the side of rhombus =29cm
therfeore,
perimeter=4*side
perimeter=(4*29) cm
perimeter=116cm