Question

Length diagonals of rhombus are in ratio 6:8 if it's perimeter is 40 cm. Find the length of the shorter diagonal

Answer 1

Let the unit be x so the diagonals are 6x and 8x
let the shorter diagonal be 6x and longer be 8x
the point of intersection of the two digonals to be named as O
so half of the diagonals be 6x/2 and 8x/2
given pmt=40cm
one side=40÷4=10 cm
so all the sides are 10cm respectively (as in Rhombus all the sides are of equal measure)

so According to pythagoras theorm
(6x/2)^2 +(8x)^2 =(10)^2
36x^2/4+64x^2/4=100
100x^2=100×4
100x^2=400
x^2=4
x=2

so length of shorter side is 6x=6×2=12

hope it helps :))

Answer 2

Answer:

R.E.F image 

Let the sides of rhombus be a

and diagonals be d1 and d2

perimeter =40cm

4a=40cm

a=10cm

Ratio of diagonals=3:4

d2d1=43

d1=43d2 ...(1)

Now,

a2=4d12+4d22

d12+d22=4a2

169d22+d22=4(10)2

1625d22=400

Square Rooting both sides

45d