Question

2.

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

Answer 1

Solution

Given :-

• The diagonals of a rhombus are in the ratio 5:12
• perimeter is 104 cm

Find :-

• the lengths of the sides and the diagonals

Explanation

Let,

Side of rhombus be x cm.

In rhombus all side be same.

Then, According to question,

➡Perimeter of rhombus = Sum of all side .

So,

➡ x + x + x + x = 104

➡ 4x = 104

➡x = 104/4

➡x = 26

Since,

All side of rhombus will be 26 cm.

(The diagonal of a rhombus are in the ratio 5:12 )

Let ,

Length of diagonal are 5y & 12y .

(Diagonal are perpendicular bisector of each other . )

Let, Here,

ABCD be the rhombus ,

where

• AB = BC = CD = DA = 26 cm
• AC = 5y (Diagonal)
• BD = 12y (Diagonal )

Now, take a triangle , ∆BCD

Using Pythagoras Theorem

➡ AB² = AO² + BO²

Keep all above values,

➡(26)² = (2.5y)² + (6y)²

➡676 = 6.25y² + 36y²

➡42.25y² = 676

➡y² = 676/42.25

➡y = √(676/42.25)

➡y = 26/6.5

➡y = 260/65

➡y = 4

Hence

• First Diagonal be AC = 5y = 5 × 4 = 20cm
• Second Diagonal be BD = 12y = 12 × 4 = 48cm

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