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Question
The perimeter of a rhombus is 52 CM if one of its diagonal is 24 cm long find the length of the diagonals other one and the area of the Rhombus
The perimeter of a rhombus is 52 CM if one of its diagonal is 24 cm long find the length of the diagonals other one and the area of the Rhombus
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Solution
Let the side be x.
perimeter of a rhombus= 4*side=4x=52cm
x=52/4= 13cm
We know that the diagonals of a rhombus bisect each other at right angles.
Let the intersecting point of diagonals be O.
Consider triangle AOB
OA=24/2=12cm
OB=√(AB²-OA²)=√(13²-12²)
=√(169-144)=√25=5cm
Then length of other diagonal BD=2*OB=2*5=10cm
Area of the rhombus=1/2*AC*BD=1/2*24*10=120cm²
perimeter of a rhombus= 4*side=4x=52cm
x=52/4= 13cm
We know that the diagonals of a rhombus bisect each other at right angles.
Let the intersecting point of diagonals be O.
Consider triangle AOB
OA=24/2=12cm
OB=√(AB²-OA²)=√(13²-12²)
=√(169-144)=√25=5cm
Then length of other diagonal BD=2*OB=2*5=10cm
Area of the rhombus=1/2*AC*BD=1/2*24*10=120cm²
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