Question

The perimeter of a rhombus is 146 cm. One of its diagonals is 55 cm. Then find the length of the other diagonal and the area of the rhombus.



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Answer 1

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

One diagonal is 55 cm the other diagonal is 48 cm. The area of the rhombus = 55*48/2 = 1320 sq cm.