The perimeter of a rhombus is 58 cm. One of the diagonal is 20 cm. What is the sum (in cm) of both the diagonals of the rhombus?
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Correct answer: A
Explanation
Perimeter = 58 cm
Side = 58 / 4 = 14.5 cm
In a rhombus, the diagonals bisect each other.
Half of the first diagonal = 20 / 2 = 10 cm
By the Pythagorean theorem,
(Second diagonal / 2)² = 14.5² - 10²
= 210.25 - 100
= 110.25
Second diagonal / 2 = 10.5 cm
Second diagonal = 21 cm
Sum of both diagonals = 20 + 21 = 41 cm