Question

The diagonals of the rhombus are in the ratio of 3:4.If the perimeter is 40 cm,find the length vof the diagonals.

Answer 1

as length of side of rhombus is p/4
so it is 10 cm

Answer 2

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↠ 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.

HOPE SO IT HELPS YOU