If Diagonals of a rhombus is 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 Diagonals of a rhombus is 10 cm and 24 cm then perimeter of the rhombus is 52 cm.
Let's find the perimeter of the rhombus
Let's draw a diagram of the rhombus with the diagonals 10cm and 24cm
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 = 13cm, perimeter of the rhombus, P = 4 × side of a rhombus
P = 4 × AB
P = 4×13 = 52 cm