ABC is an equilateral triangle with side 12cm

AE⊥BC

In ABD andACD

∠ADB=∠ADC=90

AB=AC=12cm

AD=AD (COMMON)

ABDACD

AD²+BD²=AB²

AD²+6²=12²

AD²+36=144

AD²=144-36

AD²=108

AD=

AD=10.39 cm