Question

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

Answer 1

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.