Question

Triangle A B C is shown. Angle A B C is a right angle. An altitude is drawn from point B to point D on side A C to form a right angle. The length of A D is x, the length of D C is 4 x, and the length of B D is 10. What is the value of x? 2 units 3 units 5 units 8 units

Answer 1

C) 5 units

Step-by-step explanation: took test on edge

Answer 2

The value of x is 5 units

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

`Perpendicular^2+Base^2 = Hypotenuse^2 \\BD^2+AD^2=AB^2\\10^2+x^2=AB^2\\100+x^2=AB^2\\(AD)/(AB)=Cos A\\(x)/(√(100+x^2))=Cos A\\(AB)/(AC)=Cos A\\(√(100+x^2))/(5x)=Cos A\\So,(x)/(√(100+x^2))=(√(100+x^2))/(5x)\\x=5 units`

Hence The value of x is 5 units