The perimeter of a rhombus is 240m and of its diagonal is 96m. Find the area of the rhombus and its other diagonal
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Answered by
13
Perimeter of rhombus = 240
4 × side = 240

side = 60 m
××××××××××××
We know, diagonals of rhombus bisects each other at 90°
By Pythagoras theorem,
(96/2)² + (half of other diagonal)² =60²
(48)² + (Half of other diagonal)² = 60²
half of other diagonal = √(60²-48²)
Half of other diagonal = √(3600-2304)
Other diagonal = 2 × 36 = 72 m
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I hope this will help you
(-:
4 × side = 240
side = 60 m
××××××××××××
We know, diagonals of rhombus bisects each other at 90°
By Pythagoras theorem,
(96/2)² + (half of other diagonal)² =60²
(48)² + (Half of other diagonal)² = 60²
half of other diagonal = √(60²-48²)
Half of other diagonal = √(3600-2304)
Other diagonal = 2 × 36 = 72 m
======================
I hope this will help you
(-:
Answered by
10
Heya !!!
Let ABCD is a rhombus.
In which ,
AB = AD = BC = CD
And,
AC and BD are its two diagonals.
Given that ,
Perimeter of rhombus = 240 m
4 × side = 240
Side = 240/4
Side = 60 m
Let AC = 96 m
We know that,
Diagonals of rhombus bisect each other other at right angle.
OA = OC = 1/2 × AC
OA = OC = 1/2 × 96 = 48
In right angled triangle OAB
(AB)² = (OA)² + (OB)²
(OB)² = ( AB)² - (OA)²
(OB)² = ( 60)² - (48)²
(OB)² = 3600 - 2304
OB² = 1296
OB = root 1296 = 36 m
Diagonal BD = 2 × OB
=> 2 × 36
=> 72 m
Therefore,
Area of rhombus ABCD = 1/2 × ( Product of diagonals )
=> 1/2 × ( AC × BD)
=> 1/2 × ( 96 × 72)
=> 6912/2
=> 3456 m².
★ ★ ★ HOPE IT WILL HELP YOU ★ ★ ★
Let ABCD is a rhombus.
In which ,
AB = AD = BC = CD
And,
AC and BD are its two diagonals.
Given that ,
Perimeter of rhombus = 240 m
4 × side = 240
Side = 240/4
Side = 60 m
Let AC = 96 m
We know that,
Diagonals of rhombus bisect each other other at right angle.
OA = OC = 1/2 × AC
OA = OC = 1/2 × 96 = 48
In right angled triangle OAB
(AB)² = (OA)² + (OB)²
(OB)² = ( AB)² - (OA)²
(OB)² = ( 60)² - (48)²
(OB)² = 3600 - 2304
OB² = 1296
OB = root 1296 = 36 m
Diagonal BD = 2 × OB
=> 2 × 36
=> 72 m
Therefore,
Area of rhombus ABCD = 1/2 × ( Product of diagonals )
=> 1/2 × ( AC × BD)
=> 1/2 × ( 96 × 72)
=> 6912/2
=> 3456 m².
★ ★ ★ HOPE IT WILL HELP YOU ★ ★ ★
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