In a rhombus of side 52 cm, one of the diagonals is 40 cm long. Find the length of the second diagonal.
Answer:
96 cm
- Let ABCD be the given rhombus whose diagonals intersect at O.
Then, AB=52 cm.
Let AC=40 cm and BD=2x cm.
- We know that the diagonals of a rhombus bisect each other at right angles. ∴ OA=12AC=20 cm,OB=12BD=x cm,and ∠AOB=90∘
- From right ΔAOB, we have AB2=OA2+OB2⟹OB2=AB2−OA2=[(52)2−(20)2] cm2=[2704−400] cm2=2304 cm2⟹ x2= 2304⟹x=√2304=48 cm.∴ OB= 48 cm.∴ BD=2×OB=2×48 cm=96 cm. Hence, the length of the second diagonal is 96 cm.