In the given figure if AD||BC, find the value of x.

Explanation

given : AD||BC
proof : in ` triangle AOD and triangleBOC`
`angle1=angle2` ( alternate angles)
` angle3= angle3` ( vertically opposite angles)

`triangleAOD ~ triangleCOB` [ AA corollary]
` Rightarrow ( AO)/(OC) = (OD)/(OB) `
` Rightarrow 3/(x-3) = (x-5)/(3x-19) `
`Rightarrow ( x-3) (x-5) = 3 ( 3x-19) Rightarrow x^2 -5x-3x+15 = 9x -57`
` Rightarrow x^(2)-17x +72=0 Rightarrow x^(2)-9x-8x+72=0`
` Rightarrow x(x-9)-8 (x-9) =0 or (x-9)(x-8)=0`
` Rightarrow x -9 =0 or x-8=0`
` Rightarrow x=9 or x=8`
Hence x= 9, 8