Answer:
x = 25
Step-by-step explanation:
From the picture attached,
ΔABC and ΔADE are the similar triangles.
Therefore, their corresponding sides will be in the same ratio.
[tex]\frac{\text{AB}}{\text{AD}}=\frac{\text{AC}}{\text{AE}}=\frac{\text{BC}}{\text{DE}}[/tex]
[tex]\frac{\text{AB}}{\text{AD}}=\frac{\text{BC}}{\text{DE}}[/tex]
And AB = AD + DB
= 2(AD) [Since, AD = DB]
By substituting these values,
[tex]\frac{\text{2AD}}{\text{AD}}=\frac{\text{34}}{\text{(x-8)}}[/tex]
2 = [tex]\frac{34}{x-8}[/tex]
x - 8 = [tex]\frac{34}{2}[/tex]
x - 8 = 17
x = 17 + 8
x = 25
