If the diagonals of a rhombus are 10 cm and 24 cm find its perimeter.
A rhombus can be defined as a diamond-shaped quadrilateral that has all four sides equal.
Answer: If the diagonals of a rhombus are 10 cm and 24 cm then the perimeter of the rhombus is 52 cm.
Let's find the perimeter of the rhombus.
Let us observe the diagram of the rhombus with the diagonals 10 cm and 24 cm.
Here, AC = 24 cm and BD = 10 cm, therefore, AO = 12 cm and BO = 5 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 = 122 + 52
AB2 = 144 + 25
AB2 = 169
AB = √169
AB = 13 cm
Since the length of one side of the rhombus is AB = 13 cm, perimeter of the rhombus, P = 4 × side of a rhombus
P = 4 × AB
P = 4 ×13 = 52 cm