Question

Given a right triangle ABC with altitude BD drawn to hypotenuse AC. If AC = 24 and DC = 6, what is the length of BC?

Answer 1

Answer:

• BC = 12

Step-by-step explanation:

BD is the altitude, it breaks ΔABC into two similar triangles:

• ΔABD ~ ΔBCD

The ratios of corresponding sides:

• AD/BD = BD/DC ⇒ BD² = AD*DC ⇒ BD² = (24 - 6)*6 ⇒ BD² = 108

On the other hand:

• BC² = BD² + DC² ⇒ BC² = 108 + 6² = 144
• BC = √144
• BC = 12