Question

The diagnols of a rhombus are in the ratio 5:12 . If it's perimeter is 104 cm , find the lengths of the sides and the diagnols​

Answer 1

★ Given :

• Perimeter of rhombus = 104 cm
• The diagonal are in ratio 5 : 12

★ To find :

• The Length of sides.
• And the Length of diagonals.

★ Solution :

Finding the side of rhombus :

Perimeter of rhombus = 104 (given)

→ 4 × side = 104

→ side = 104/4

→ side = 26cm

Now,

Let's assume Diagonals as :

• 5x (AC)
• 12x (BD)

Therefore,

• OC will be = 5/2x

• And OD will be = 12/2x = 6x

Thus, here we can observe a right angled triangle ∆DOC.

Thus By Pythagorean theorem :

⟼ (DC)² = (OD)² + (OC)²

⟼ (26)² = (6x)² + (5/2x)²

⟼ 676 = 36x² + 25/4 x²

⟼ 676 = 144x² + 25x²/4

⟼ 676 = 169x²/4

⟼ 676×4 = 169x²

⟼ 2704 = 169x²

⟼ x² = 2704/169

⟼ x² = 16

⟼ x = √16

⟼ x = √4×4

⟼ x = 4

Therefore the measure of the diagonals :

• AC (5x) = 5 × 4 = 20cm
• BD (12x) = 12 × 4 = 48 cm

And the length of the side :

• Side of rhombus = 26 cm i.e. AB = BC = CD = DA = 26 cm because all sides of rhombus are equal.