Question

. The diagonals of a rhombus are 24 cm and 32 cm. Find the perimeter of the
rhombus.
(1) 40 cm
(3) 100 cm
(2) 80 cm
(4)120 cm​

Answer 1

Answer:

80 cm

Step-by-step explanation:

in the figure, Let AC be 32 cm

and BD be 24 cm

since diagonals of rhombus bisect at right angles:

AO=OC=32÷2=16 cm

Od=OB=24÷2=12 cm

and Angle AOD=90°

in right ∆ AOD, by pythagoras theorem,

${(16)}^{2} + ( {12)}^{2} = h ^{2} \\ 256 + 144 = {h}^{2} \\ 400 = {h}^{2} \\ \\ \sqrt{400} = h \\ \\ h = 20$

therfore side= 20 cm

perimeter = 20×4=80 cm

Answer 2

Answer: 80cm

Step-by-step explanation:

If rhombus is abcd and diagonals cross on point o then,

d1 = 32 , d2 = 24

Half of diagonal is = 16,12

In triangle abo,

paithogorus theorum,

(hy)square=(hei)square + (base)sq.

(hy)sq. = 16sq.+ 12sq.

hy sq. = 256 + 144

hy sq. = 400

hy. = 20

One side of rhombus is=20

perimeter = 4*20= 80 cm