Question

How do I find the missing side length?

Answer 1

check the picture below.


`\bf 8√(6)=a√(2)\implies \cfrac{8√(6)}{√(2)}=a\implies \stackrel{rationalizing~it}{\cfrac{8√(6)}{√(2)}\cdot \cfrac{√(2)}{√(2)}}=a\implies \cfrac{8√(12)}{2}=a \\\\\\ 4√(12)=a\implies 4√(2^2\cdot 3)=a\implies \boxed{8√(3)=a}\\\\ -------------------------------`


`\bf 2b=a\implies b=\cfrac{a}{2}\implies b=\cfrac{8√(3)}{2}\implies \boxed{b=4√(3)}\\\\ -------------------------------\\\\ x=b√(3)\implies x=4√(3)\cdot √(3)\implies x=4√(3^2)\implies \boxed{x=12}`