SAT Math: Right Triangle Altitude CD to Hypotenuse AB (AD = 4, DB = 16), Find CD

Exact Question Text

In right triangle ABC, angle C is 90 degrees. Altitude CD is drawn to hypotenuse AB such that AD = 4 and DB = 16. What is the length of CD?

1. Step-by-Step Formal Solution

1. Triangle ADC ~ Triangle CDB.
2. AD / CD = CD / DB => (CD)^2 = AD * DB.
3. (CD)^2 = 4 * 16 = 64 => CD = 8.

2. Fast Desmos / Calculator Shortcut

Evaluate sqrt(4 * 16) in Desmos => 8.

3. Distractor Trap Analysis

• Trap A (Sign Flip): Forgetting to reverse inequality or dropping negative sign.
• Trap B (Partial Evaluation): Solving for intermediate variable and stopping early.
• Trap C (Extreme Assumption): Over-inferring beyond textual evidence.
• Option Correct: Accurately satisfies all algebraic and logical constraints.