Question

Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AC = 6 and DC = 4, what is the length of BC in simplest radical form?

a) 6√2
b) x
c) 4√2
d) None of these

Answer 1

To find the length of BC in a right triangle, we can use the Pythagorean theorem. By substituting the given values, solving for BC, and simplifying the radical, we find that BC is approximately 4.5.

Step-by-step explanation:

To find the length of BC, we can use the Pythagorean theorem, which relates the lengths of the legs of a right triangle to the length of the hypotenuse. In this case, the hypotenuse is AC and the leg lengths are BD and DC.

According to the theorem, AC² = BD² + CD². Substituting the given values, we get 6² = BC² + 4².

Solving for BC, we have BC² = 36 - 16 = 20.

Taking the square root of both sides, we get BC = √20.

Simplifying this radical, we find that BC is approximately equal to 4.5. Therefore, the correct answer is d) None of these.