Answer:
x = 6
Step-by-step explanation:
For the triangles to be similar then the ratios of corresponding sides would be equal, that is
[tex]\frac{DF}{XZ}[/tex] = [tex]\frac{DE}{XY}[/tex] , substitute values
[tex]\frac{3(x-1)}{7.5}[/tex] = [tex]\frac{10}{x-1}[/tex] ( cross- multiply )
3(x - 1)² = 75 ( divide both sides by 3 )
(x - 1)² = 25 ( take the square root of both sides )
x - 1 = ± [tex]\sqrt{25}[/tex] = ± 5 ( add 1 to both sides )
x = 1 ± 5 , then
x = 1 + 5 = 6 or x = 1 - 5 = - 4
But x > 0 then x = 6
For the triangle to be similar then x = 6
