The two diagonals of a rhombus are respectively, 14 cm and 48 cm. The perimeter of the rhombus is equal to:
Show answer & explanation
Correct answer: D
Explanation
Correct Answer is option 4 i.e. 100 cm
Diagonals of a rhombus bisect each other at 90°
Length of diagonals:
AC = 48 cm and BD = 14 cm
Then,
AO = OC = 48/2 = 24 cm
BO = OD = 14/2 = 7 cm
In right angle triangle AOB:
AB2 = OA2 + OB2
⇒ AB2 = 242 + 72
⇒ AB2 = 576 + 49
⇒ AB2 = 625
⇒ AB = 25
Hence,
Perimeter of rhombus = 25 × 4 = 100 cm