Question

the diagonals of a rhombus are in the ratio 5:12. If its perimeter is 104 cm, find the length of the sides and the diagonals​

Answer 1

Answer:

48 cm

Step-by-step explanation:

Rhombus all 4 side are equal

X+x+x+x = 104

4x= 104

X= 26 cm

Now diagonals of rhombus bisect each other at 90 then

26² = (5x)²+(12x)²

676 = 25x² + 144x²

676 = 169x²

X² = 676/169

X²= 4

X = 2

Hence 5*2 = 10 and 12*2= 24 …Hence full length of diagonals are 10+10 = 20 and 24+24=48

Answer 2

Answer:

The length of the sides is 26 cm and the diagonals are 10 cm and 24 cm...

Step-by-step explanation:

Given :

Diagonal of a rhombus are in ratio 5:12        

Perimeter = 104 cm

Let the length of all sides of Rhombus be 'x' .  

Perimeter = Sum of all sides

-Perimeter = x + x + x + x

-104 = 4x

-x = 104/4

-x= 26 cm

∴,Length=26 cm

So,

Let the diagonal of rhombus be 5y and 12y

By Pythagoras theorem,

a²=b²+c²

-(26)² = (5y)² + (12y)²

-676 = 25y² + 144y²

-676 = 169y²

-y² = 676/169

-y² = 4

-y = √4

∴ y = 2

So,

-5y  = 5 × 2 = 10 cm

-12y  = 12 × 2 = 24 cm

∴ ,Diagonals=10 cm and 24 cm