Question

THE DIAGNOLS OF A RHOMBUS ARE IN THE RATIO 5:12.IF ITS PERIMETER IS 104 CM,FIND THE LENGTHS OF SIDES AND THE DIAGNOLS

Answer 1

Its perimeter is 104cm

Perimeter =4xside=104

=> side =26cm

The diagonals of a rhombus are in the ratio 5:12.

Let diagonals are 5x and 12x

Diagonals of rhombus are perpendicular to each other, so by applying Pythagoras theorem

$= > \: {a}^{2} = ( \frac{ {5x}^{2} }{2} ) \: + ( \frac{ {12x}^{2} }{2} )$

$= > \: {26}^{2} \: = \frac{ {169x}^{2} }{4}$

$= > \: x = 4$

Diagonals are 5x=20cm and 12x=48cm