Answer:
[tex]x= (3, \frac{3}{10} )[/tex]
Step-by-step explanation:
The figure is composed of two similar triangles; therefore,
[tex]\frac{7x}{19x-4} =\frac{7x+8}{(5x+5)+(19x-4)}[/tex] this says the ratio of the sides is same for the two triangles.
we simplify and a rearrange to get
[tex]7x(24x+1)=(7x+8)(19x-4)[/tex]
which we expand and get
[tex]168x^2+7x=133x^2+124x-32[/tex]
[tex]35x^2-117x+32=0[/tex]
this quadratic equation has solutions
[tex]x=3.04[/tex]
[tex]x=0.30[/tex]
As integers and simplified fractions these are
[tex]x= (3, \frac{3}{10} )[/tex]
