Question

the perimeter of rhombus is 20 CM and one of its diagonal is 6m long. Find the length of the other diagonal.

Answer 1

Perimeter = 20 cm.

Since all sides of the rhombus are equal, so each side of the rhombus= 20 cm/4 = 5 cm.

The diagonals of a rhombus bisect each other at right angle. Therefore, the diagonals divide the rhombus in 4 equal right triangles, whose hypotenuse are the sides of the rhombus, and other two sides are the half lengths of the two diagonals.

In one such right triangle, hypotenuse = 5 cm, side 1 = 6 cm/2 = 3 cm

Therefore, side 2 of the right triangle= [ 5² -3²]½= 4 cm.

Therefore length of the second diagonal = 2×4 cm = 8 cm.

Answer 2

Answer:

Other diagonal = 8 cm

Step-by-step explanation:

Let the rhombus be ABCD;

Perimeter of rhombus=20 cm

4*side=20

side=20/4

side=5cm

As we know ,the properties of rhombus;

rhombus bisect the diagonals & make  right angle

 so,AB=5cm, Digonal  AO=3cm

By pythagroras theorem;

AB^2=AO^2+OB^2

5^2=3^2+OB^2

OB^2=25-9

OB^2=16

OB=4 cm

OB+OD=8cm

That is = to other diagonal;

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