### If area of a rhombus is 384 cm^{2} and one of its diagonal is 24 cm, find its perimeter.

**Answer:**

80 cm

**Step by Step Explanation:**

- We know that the area of the rhombus =
Product of diagonals of the rhombus 2

It is given that one diagonal of the rhombus = 24 cm.

Let the other diagonal of the rhombus be**b**cm. Then,

384 =24 × b 2

⇒ 384 × 2 = 24 × b

⇒ b =768 24

⇒ b = 32 - Let us consider one of the right angle triangles formed by the diagonals. Since we know that the diagonals of a rhombus bisect each other, we can say that one of the sides is of length

cm = 12 cm and the other side is24 2

cm = 16 cm long.32 2 - Let the hypotenuse which is the third side of the triangle and also one of the sides of the rhombus be S cm. Then, by the Pythagoras theorem,

S^{2}= (12)^{2}+ (16)^{2}

S^{2}= 144 + 256

S^{2}= 400

S = √400

S = 20 - Perimeter of the rhombus = 4S

4 × 20

= 80 - Therefore, the perimeter of the rhombus is
**80 cm.**