If area of a rhombus is 384 cm2 and one of its diagonal is 24 cm, find its perimeter.
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Step by Step Explanation:
- We know that the area of the rhombus =
|Product of diagonals of the rhombus|
It is given that one diagonal of the rhombus = 24 cm.
Let the other diagonal of the rhombus be b cm. Then,
⇒ 384 × 2 = 24 × b
⇒ b =
⇒ 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 is cm = 16 cm long.
- 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,
S2 = (12)2 + (16)2
S2 = 144 + 256
S2 = 400
S = √400
S = 20
- Perimeter of the rhombus = 4S
4 × 20
- Therefore, the perimeter of the rhombus is 80 cm.