Answer:
The value of x is 5 units
Step-by-step explanation:
We are given that triangle ABC is right angled triangle
An altitude is drawn from point B to point D on side A C to form a right angle.
Length of AD = x
Length of DC = 4x
Length of BD = 10
In triangle ABD
[tex]Perpendicular^2+Base^2 = Hypotenuse^2 \\BD^2+AD^2=AB^2\\10^2+x^2=AB^2\\100+x^2=AB^2\\\frac{AD}{AB}=Cos A\\\frac{x}{\sqrt{100+x^2}}=Cos A\\\frac{AB}{AC}=Cos A\\\frac{\sqrt{100+x^2}}{5x}=Cos A\\So,\frac{x}{\sqrt{100+x^2}}=\frac{\sqrt{100+x^2}}{5x}\\x=5 units[/tex]
Hence The value of x is 5 units
