Answer:
x = 5
Step-by-step explanation:
This uses the altitude on hypotenuse theorem
The 2 triangles formed are similar to the given triangle and to each other.
Δ ADB ~ Δ BDC
Since the triangles are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{DB}{DC}[/tex] = [tex]\frac{AD}{BD}[/tex] , substitute values
[tex]\frac{10}{4x}[/tex] = [tex]\frac{x}{10}[/tex] ( cross- multiply )
4x² = 100 ( divide both sides by 4 )
x² = 25 ( take the square root of both sides )
x = [tex]\sqrt{25}[/tex] = 5
