Question

the lengths of the diagonals of a rhombus are in the ratio 6:8. If its perimeter is 40cm . Find the length of the shower diagonal

Answer 1

As we know that the perimeter of rhombus = 4 × side

 

Here,

 

40 = 4 × side

 

40/4 = side

 

10 side

 

then,

 

Let the length of diagonals be 6x and 8x

 

by pythagoras theorem,

 

10^2 = (6x/2)^2 +(8x/2)^2

 

100 = 9x^2 + 16x^2

 

100 = 25x^2

 

100/25 = x^2

 

4  = x^2

 

2= x

 

Now,

 

length of diagonals is:-

 

6 × 2 =12cm

 

and

 

8 × 2 =16cm

 

 

Length of shorter diagonal is 6x i.e. 12cm 

Hope This Helps :)