Question

the lenght of the diagonals of rhombus are 24 and 32 cm .calculate the lenght of altitude

Answer 1

Answer:

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