Question

the diagonals of a rhombus are in the ratio 3:4 if the perimeter is 40 cm find the length of side by diagonals of the Rhombus​

Answer 1

Let the length of the side of the rhombus be x

Since the sides of a rhombus are equal,

4x=40

x=40/4

=10 cm

let the diagonals d1 and d2 of a rhombus be 3y and 4y respectively.( since the ratio of the diagonals are given as 3:4)

Diagonals of a rhombus are perpendicular bisectors.

Therefore a rhombus can be divided into four right triangles.

Considering a triangle from the rhombus,

By Pythagoras theorem,

x^2 = (d1/2)^2 + (d2/2)^2

10^2 = (3y/2)^2 + (4y/2)^2

100 = (9(y^2))/4 + (16(y^2))/4

400 = (9+16) (y^2)

400 = 25 (y^2)

y^2 = 400/25

y^2 = 16

y = 4

therefore the diagonals of the rhombus are:

d1 = 3y = 3 *4 = 12 cm

d2 = 4y = 4 *4 = 16 cm

the length of the side of the rhombus is 10 cm and the diagonals d1 and d2 are 12 cm and 16 cm respectively.