Question

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 1

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, $A{B}^2=O{A}^2+O{B}^2$
[Pythagoras theorem]
⇒ $A{B}^2=(8{)}^2+(6{)}^2$
⇒​ $A{B}^2=64+36=100$
⇒​ AB =​ 10 cm
Hence, the side of the rhombus is 10 cm.
PA