20. PORS is a rhombus whose diagonals are in the
ratio 3:4. If its perimeter is 40 cm,
find the length of diagonals of the rhombus.
Answers
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.