Question

The diagonal of a rhombus are in a ratio5:12
and its perimeter is 104 cm. Find the
length of its diagonals​

pls tell the answer

Answer 1

Answer:

Given :

Perimeter = 104 cm

Ratio = 5:12

To Find :

Length of diagonal

Solution :

Side = Perimeter of rhombus ÷ 4

Side = 104 ÷ 4

Side = 26 cm

Let,

Diagonal 1 = 5x

Diagonal 2 = 12x

Since diagonal bisect each other

Diagonal 1/2

5x/2

Diagonal 2/2

12x/2

6x

By using Pythagorean theorem

(26)² = (5x/2)² + (6x)²

676 = 25x²/4 + 48x²

676 = 25x² × 48x²/4

676 = 169x²/4

676 × 4 = 169x²

1352 = 169x²

1352/169 = x²

16 = x²

√16 = x

4 = x

Diagonal are

5 × 4 = 20 cm

12 × 4 = 48 cm