The perimeter of a rhombus is 146 cm and one of its diagonals is 48 cm, find the other diagonal and the area of the rhombus.
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we know that,the diagonals of rhombus bisect each other at 90°.
the half of the diagonal =48×1/2=24cm
the each side=146/4=36.5cm
the haf of the other diagonal=√(36.5^2-24^2)=27.5cm
the length of the diagonal=27.5×2=55
the half of the diagonal =48×1/2=24cm
the each side=146/4=36.5cm
the haf of the other diagonal=√(36.5^2-24^2)=27.5cm
the length of the diagonal=27.5×2=55
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The perimeter of a rhombus is 146 cm and one of its diagonals is 48 cm, find the other diagonal and the area of the rhombus.
Given :-
- The perimeter of a rhombus = 146 cm
- One of its diagonal = 48 cm.
To Find :-
- Other diagonal of rhombus
- Area of the rhombus.
Solution :-
We know that, all sides of rhombus are equal.
Perimeter of rhombus = 146 cm
Diagonals in a rhombus bisect each other at right angles. O is the midpoint of AC and BD. But BD = 55. therefore, OB = OD = 27.5 cm
In △AOB
∠AOB = 90°
By Pythagoras theorem,
We know,
Also,
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