Question

What is the value of x?​

Answer 1

The top smaller sub-triangle and the whole big triangle are similar. This means that the correspondant sides are in proportion. So, we have

$6\div 5 = 54\div 3x+12$

Which implies

$6(3x+12)=5\cdot 54 \iff 3x+12=\dfrac{5\cdot 54}{6}=45$

So, we have

$3x+12 = 45 \iff 3x = 33 \iff x=11$