Question

The perimeter of a rhombus is 40 cm . If one of the diagonal is 16 cm than find the other diagonal and the area of the rhombus.

Answer 1

Let the side of the rhombus be x cm.

Perimeter =(4×x) cm =>4x cm

According to the question,
4x=40
x=10

Now,as we know that the diagonals of a rhombus bisect each other at 90°, it forms 4 right angled triangles .

Here,
AO is the height.
BO is the base which is of 8cm
AB is the hypotenuse which is of 10cm

Using Pythagoras theorem,
(BO)^(2) +(AO)^(2)= (AB)^(2)
8^(2) + (AO)^(2)=10^2
64 + (AO)^(2)=100
(AO)^(2) = 100-64
(AO)^(2)=36
AO= 36^(1/2)
AO =6 cm

Therefore ,the other diagonal is (2×6) cm=12 cm


Now ,the area of the rhombus = (1/2×12×16) cm sq
=>96 cm sq