Question

Pqrs in a rhombus
Whose diagonal are in the ratio 3:4.if it is perimeter is 40 cm.find the length of diagonal of the rhombus

Answer 1

Answer:

Side of rhombus is congruent,

perimeter of rhombus=4(side)

40=4(side)

10=side

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.