Question

diagonal of a rhombus are in the ratio 5 is to 12 if the perimeter is 104 cm find the length of the side and the diagonals

Answer 1

Rombus all 4 side are equal

X+x+x+x = 104

4x= 104

X= 26 cm

Now diagonals of rombus 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

$\huge\sf{\underline{\underline{Answer}}}$

Given :

• Diagonal of a rhombus are in ratio 5:12

       

• Perimeter = 104 cm

To find :

• The lengths of the sides

•  The lengths of the diagonals

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

Rhombus has 4 sides.

Perimeter = Sum of all sides

⇒Perimeter = x + x + x + x

⇒104 = 4x

⇒x = 104/4

∴ x = 26 cm

Now, we have lengths of all side which is 26 cm.

So,

Let the diagonal of rhombus is 5y and 12y

  Diagonals of  rhombus bisect each other at 90°

By pythagoras theroum

⇒(26)² = (5y)² + (12y)²

⇒676 = 25y² + 144y²

⇒676 = 169y²

⇒y² = 676/169

⇒y² = 4

⇒y = √4

∴ y = 2

Here we get the value of y

5y (put the value of 'y')

5 × 2 = 10 cm

12y (put the value of 'y')

12 × 2 = 24 cm

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