1
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
Open in App
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
Suggest Corrections
2
Similar questions
View More
Join BYJU'S Learning Program
Explore more
Join BYJU'S Learning Program
