What is the perimeter of a rhombus whose diagonals are 16 cm and 30 cm?
A rhombus has four equal sides.
Answer: The perimeter of a rhombus whose diagonals are 16 cm and 30 cm is 68 cm.
Let's find the side of the rhombus first then perimeter.
Let's draw a diagram of the rhombus with the diagonals 16 cm and 30 cm
So AC = 30 cm and BD = 16 cm
Therefore, AO = 15 cm and BO = 8 cm
Now to find the perimeter, we need the length of AB.
Let's find AB using the pythagoras theorem in △ABC,
AB2 = AO2 + OB2
AB2 = 152 + 82
AB2 = 225 + 64
AB2 = 289
AB = √289
AB = 17 cm
Therefore the length of one side of the rhombus is AB = 17 cm.
The Perimeter of the rhombus: P = 4 × length of the side
P = 4 × 17 cm
P = 68 cm