Answer:
See below
Step-by-step explanation:
[tex]1.\:\:\overline{BD}||\overline{AE}[/tex]
(By Midsegment theorem)
[tex]2.\:\:m\angle 1=48\degree\implies m\angle 4=48\degree [/tex]
([tex]\angle 1\: \&\:\angle 4[/tex] are alternate angles)
[tex]3.\:\:m\angle 3=25\degree\implies m\angle 2=25\degree [/tex]
([tex]\angle 2\: \&\:\angle 3[/tex] are vertical angles)
[tex]4.\:\:\overline {AE}=17\: cm\implies BD = 8.5\: cm [/tex]
(By midsegment theorem: [tex]BD=\frac{1}{2}AE[/tex]
[tex]5.\:\: BD=\frac{1}{2}AE\\\\\implies (3x+10)=\frac{1}{2}\times (12x+2)\\\\\implies 2(3x +10) = 12x+2\\\\\implies 6x +20= 12x+2\\\\\implies 6x - 12x = 2-20\\\\\implies -6x =-18\\\\\implies x =\frac{-18}{-6}\\\\\implies x = 3\\\\\implies \overline{BD}= (3\times 3 + 10)\\\\=(9+10)\\\\\implies \overline{BD}= (9 + 10)\\\\\implies \huge{\purple{\overline{BD}=19}}[/tex]
