Question

the area of a rhombus 28 sq.cm.If one diagonal is of length 32 cm, find the length of the other diagonal.​

Answer 1

Let ABCD be a rhombus with AC and BD as its diagonals.

We know that the diagonals of a rhombus bisect each other at right angles.

Let O be the intersecting point of both the diagonals.

Let AC=24cm and BD=32cm

OA=AC/2

OA= 24/2=12cm

OB=BD/2

OB=32/2=16cm

In rt.ΔAOB by Pythagoras theorem we have

AB²=OA²+OB²

=(12)²+(16)²

=144+256

=400

AB=20cm

Hence, each side of the rhombus is of length 20cm

Area of rhombus=1/2*AC*BD

=1/2*24*32

=12*32

Area of rhombus=base*altitude

12*32=20*h

19.2cm=h

Answer 2

area if the Rhombus = 28cm^2

--> 1/2 × d1 × d2 = 28cm^2

--> 1/2 × 32 × d2 = 18cm^2

--> 16 × d2 = 18cm^2

--> d2 = 18/16

--> d2 = 9/8

--> d2 = 1.125cm

thus, the Length of the other diagonal of the Rhombus is 1.125cm