The diagonal of a rhombus are in a ratio5:12and its perimeter is 104 c

1.	The diagonal of a rhombus are in a ratio5:12and its perimeter is 104 cm. Find thelength of its diagonalspls tell the answer
Answer» 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

The diagonal of a rhombus are in a ratio5:12and its perimeter is 104 cm. Find thelength of its diagonalspls tell the answer

Answer»

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

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

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