Answer:
X = 16
Step-by-step explanation:
Notice that we are in the presence of two similar triangles, one larger than the other. The larger triangle is AED, and the smaller one is ACB.
Since there are similar triangles, we can write a proportionality between their known sides:
[tex]\frac{side\,\,AD}{side\,\,AB} =\frac{side\,\,ED}{side \,\,CB}[/tex]
notice that AD = x + 6
AB = x
ED = 11
CB = 8
So now we can re-write the proportion and solve it for the unknown "x":
[tex]\frac{side\,\,AD}{side\,\,AB} =\frac{side\,\,ED}{side \,\,CB} \\\\\frac{x+6}{x} =\frac{11}{8} \\8\,(x+6)=11\,x\\8\,x\,+\,48=11\,x\\48=11\,x-8\,x\\48=3\,x\\x=\frac{48}{3} \\x=16[/tex]
