Area of a rhombus is 720 square cm. Side of the rhombus is 41 cm. What is the sum (in cm) of its diagonals?
Show answer & explanation
Correct answer: B
Explanation
Let x and y be the halves of the two diagonals.
Area = 2xy
720 = 2xy
xy = 360
The diagonals of a rhombus bisect each other at right angles.
x² + y² = 41² = 1681
(x + y)² = x² + y² + 2xy
= 1681 + 720
= 2401
x + y = 49
Sum of both full diagonals = 2(x + y)
= 2 × 49 = 98 cm.