Question

The perimeter of a rhombus is 52 cm and one diagonal is 24 cm . what is the length of the other diagonal

Answer 1

The perimeter of rhombus is 52 cm
                Measure of one side = 52/4
                                                  = 13 cm
 
                                  Half of d1 = 12 cm
                                  Half of d2² = 13²-12²
                                                    =√(169-144)
                                                    = √25
                                                    = 5 cm   
                                               d2 = 2*5 = 10 cm

Therefore, the measurement of other diagonal is 10 cm.

Hope this helpz :)

Answer 2

Heya !!!

Let ABCD is a rhombus.

In which,

AC and BD are it's diagonals.

Let AC = 24 cm

Perimeter of rhombus = 52 cm

4 × Side = 52 cm

Side (AB) = 52/4 = 13 cm

We know that,

The diagonals of a rhombus bisect each other at right Angles.

Therefore,

OA = OC = 1/2 × AC = 1/2 × 24 = 12 cm

By pythagoras theroem,

AB = (OA)² + (OB)²

13² = (12)² + (OB)²

169 = 144 + OB²

OB² = 169-144

OB² = 25

OB = ✓25 = 5 cm

Therefore,

Diagonal BD = 2 × OB = 2 × 5= 10 cm

HOPE IT WILL HELP YOU.... :-)