The diagonals of the rhombus are in the ratio 3 4 the perimeter of the rhombus is 40cm find the lengths of the sides and of the diagonals?

The length of the sides of the rhombus are 10cm, as a rhombus has equal sides.

since the diagonals of a rhombus are perpendicular,

ratio of

side of rhombus to

1/2 a diagonal to

1/2 of another diagonal

is 5:4:3 (pythagorean thriple),

hence ratio of side of rhombus to

1 diagonal

to another diagonal

is 5:8:6.

since 5 units = 10cm

8 units = 16cm

6 units = 12cm

and there are your diagonals.