Question

the diagonals of a rhombus are in the ratio 3:4. if its perimeter is 40 cm .find its length of the sides and dioganals of the rohumbus..

Answer 1

Let the meet of ratio be x.

Since side^2 = (d1)/2)^2 + (d2/2)^2

=) s^2 = (3x/2)^2 + (4x/2)^2

=) s^2 = (1.5x)^2 + (2x)^2

=) s^2 = 2.25x^2 + 4x^2

=) s^2 = 6.25 x^2

=) s^2 = ( 2.5x) ^2

=) s = 2.5x

Since Perimeter of rhombus = 4* side

=) 4* side = 40cm

=) Side = 40/4

= 10cm.

Hence 2.5x = 10cm

=) x = 10/2.5 = 4cm

Hence diagnals of rhombus are 3x and 4x

= 3*4 cm and 4*4cm

= 12cm and 16cm.

Hope it's helpful to u.