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

Question

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

Philoid · Accepted Answer

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

In ΔAOB

BO =

Using pythagorous theorem in ΔAOB

AB² = AO² + BO²

10² = AO² + 8²

100-64 = AO²

AO² = 36

AO = = 6cm

Therefore length of diagonal AC of rhombus ABCD is 6 × 2 = 12cm.