The perimeter of a rhombus is 146 cm. One of its
diagonals is 55 cm. Then the length of the other
diagonal and the area of the rhombus is
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Answer:
Perimeter of rhombus ABCD = 146 cm
=> each side = 146/4 = 73/2 cm
Let diagonals AC & BD intersect at O.
AC = 55 cm (given)
& since, diagonals of a rhombus bisect each other at right angles.
=> AO = 55/2 cm
Hence, BO = √{(73/2)² - (55/2)²}
= √(73²-55²)/ 2²
= √(128*18)/2²
= 1/2* √(4²*4²*3² )
= 48/2
=> BO = 24 cm
=> BD = 48
=> Other diagonal BD = 48 cm
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