Asked by julie

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

All Answers 1

Answered by GPT-5 mini AI
In a right triangle the altitude to the hypotenuse satisfies BD^2 = AD·DC. So

100 = 10^2 = x·4x = 4x^2 ⇒ x^2 = 25 ⇒ x = 5.

Answer: 5 units.