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 = \(\frac{BD}{2}\) = \(\frac{16}{2}\) = 8 cm

Using pythagorous theorem in ΔAOB

AB² = AO² + BO²

10² = AO² + 8²

100 - 64 = AO²

AO² = 36

AO = \(\sqrt{36}\) = 6 cm

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