Question

The perimeter of a rhombus is 146 cm.One of its diagonal is 55cm.Find the area of rhombus.

Answer 1

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 = 48cm

Area of rhombus= (D1+D2)/2
=(48+55)/2
=103/2
=51.5cm2

Answer 2

Let the side of rhombus be x cm
Then, perimeter =4 *side
146=4*X
146/4=X
36.5 =X
Now in diagonal AC =55cm
then ,,,,,,AO =55/2
AO =27.5cm
In Triangle AOB,,,,, OB
$ob \: = \sqrt{ab ^{2} - {ao}^{2} }$
$ob = \sqrt{ {36.5}^{2} - {27.5}{2}$
$ob = 1332.25 - 756 .25$
ob=576 cm