The lengths of the diagonals of a rhombus are 16 cm and 12 cm. The length of each side of the rhombus is
(a) 10 cm
(b) 12 cm
(c) 9 cm
(d) 8 cm
(a) 10 cm
Explanation:
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Let ABCD be the rhombus.
∴ AB = BC = CD = DA
Here, AC and BD are the diagonals of ABCD, where AC = 16 cm and BD = 12 cm.
Let the diagonals intersect each other at O.
We know that the diagonals of a rhombus are perpendicular bisectors of each other.
∴ ∆AOB is a right angle triangle, in which OA = AC /2 = 16/2 = 8 cm and OB = BD/2 = 12/2 = 6 cm.
Now, AB2 = OA2 + OB2 [Pythagoras theorem]
⇒ AB2 = (8)2 + (6)2
⇒ AB2 = 64 + 36 = 100
⇒ AB = 10 cm
Hence, the side of the rhombus is 10 cm.
Explanation:
Let ABCD be the rhombus.
∴ AB = BC = CD = DA
Here, AC and BD are the diagonals of ABCD, where AC = 16 cm and BD = 12 cm.
Let the diagonals intersect each other at O.
We know that the diagonals of a rhombus are perpendicular bisectors of each other.
∴ ∆AOB is a right angle triangle, in which OA = AC /2 = 16/2 = 8 cm and OB = BD/2 = 12/2 = 6 cm.
Now, AB2 = OA2 + OB2 [Pythagoras theorem]
⇒ AB2 = (8)2 + (6)2
⇒ AB2 = 64 + 36 = 100
⇒ AB = 10 cm
Hence, the side of the rhombus is 10 cm.