Question

The diagonals of the rhombus are in the ratio of 3:4 if the perimeter is 40cm find the length of the diagonals

Answer 1

let each side be of x cm
then for the peri
x+x+x+x=40
4x=40
x=10
each side is of 10 cm
ratio of diagonal is 3:4
then let the diagonal be 3x and 4x
now diagonal of rhombus bisect each other at 90
then
by Pythagoras theorem
(10)^2=(3x/2)^2+(4x/2)^2
100=9x^2/4+16x^2/4
400=25x^2
400/25=x^2
20/5=x
x=4
diagonal
4x=16
3x=12