Question

ABCD is a rhombus whose diagonals intersect at O. If AB=10cm, diagonal BD=16cm, the length of diagonal AC is​

Answer 1

Answer:

Side of Rhombus are  equal.

AB = BC = CD = DA

∴AC=4×(side)2−(DiagonalBD)2

AC=4×(10)2−(16)2

=400−256

=144

=12cm

Answer 2

We know in rhombus diagonals bisect each other at right angle.

In ΔAOB

BO = BD/2 = 16/2 = 8cm

Using Pythagoras theorem

in ΔAOB

AB² = AO²+ BO²

10²= AO² + 8²

100-64 = AO²

AO² = 36

AO = √36 = 6cm

∴ Length of diagonal AC is 6 × 2 = 12cm.