Question

the length of two diagonals of a rhombus are 18cm 24cm respectively. find the length of each sind of the rhombus.

Answer 1

We can see that when the diagonals of a rhombus are drawn it divides the rhombus into 4 right triangles.

So, now we know the measure of the diagonals and we can find the adjacent and opposite sides of the right triangle by dividing the diagonals by 2 as they divide themselves into 2 equal halves.

So, the arms will be 18/2 and 24/2 cm respectively = 9 cm and 12 cm.

According to Pythagorean theorem:

Hypotenuse = √Arm₁²+Arm₂².
= √9²+12².
=√81+144.
= √225.
= 15 cm.

Sox therefore as we know that all the sides of a rhombus are equal and we know the length of 1 side, we can say that the measure of the sides of the rhombus with diagonals 18 cm and 24 cm is 15 cm.

Answer 2

Let a rhombus ABCD as shown in figure

AC = 18cm

BD = 24cm

We know that diagonals of a rhombus bisects each other.

So,

AO = 9cm

BO = 12 cm

Again,we know that diagonals of rhombus are perpendicular to each other,Therefore, AOB is right angle triangle.

Using Pythagoras theorem,

AB² = AO² + OB²

= 9² + 12²

= 81 + 144

AB² = 225

AB = 15cm

We also know that all sides of rhombus are equal.

Hence,

AB = BC = CD = AD = 15 cm