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
ANSWER:
(a) 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.
PA