We can start with evaluating the length of AD by using the Pythagorean Theorem.
C
Practice makes perfect
Let's take a look at the given diagram. It is a given that AD is perpendicular to BC, and AB is perpendicular to AC. Let x be the length of AD and y be the length of DC.
Our first step will be to evaluate the value of x. Since we are dealing with a right triangle and we already know the measures of two side lengths, let's use the Pythagorean Theorem. According to this theorem, the sum of the squared legs of a right triangle is equal to its squared hypotenuse.
The altitude drawn to the hypotenuse of a right triangle separates the hypotenuse into two segments. The length of this altitude is the geometric mean between the lengths of these two segments.
Using this theorem, we can solve for the value of y.
Since we are asked to find the length of BC, we will add the lengths of BD and DC, according to the Segment Addition Postulate.
BC=5+15=20
The length of BC is 20. This corresponds with answer C.
