Question

The area of rhombus is 112sq and length of one diagnol is 32cm and the second diagnol is 36cm true/false

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

SO, FALSE