The perimeter of a rhombus is 68 cm. One of the diagonal is 16 cm. What is the sum (in cm) of both the diagonals of the rhombus?
Show answer & explanation
Correct answer: D
Explanation
Perimeter of the rhombus = 68 cm
Side of the rhombus = 68 ÷ 4 = 17 cm
Half of the first diagonal = 16 ÷ 2 = 8 cm
Half of the second diagonal = x cm
17² = 8² + x²
289 = 64 + x²
x² = 225
x = 15 cm
Second diagonal = 2 × 15 = 30 cm
Sum of both diagonals = 16 + 30 = 46 cm