Question

Abcd is a rhombus whose diagonals ac and bd intersect at a point o. If side ab=10cm and diagonal bd=16cm, find the length of diagonal ac

Answer 1

Answer:

12 cm

Step-by-step explanation:

In a rhombus, all the sides are equal and diagonals bisect each other at 90°. Since diagonals bisect each other, AO=OC and DO=OB=8cm. By Pythagoras theory:

AO^2+OB^2=AB^2

AO^2+8^2=10^2

AO^2+64=100

AO^2=100-64

AO^2=36

AO=square root of 36=6cm

Since AO=OC

therefore, OC=6cm

And hence, AC=6+6=12cm