Triangle ABC is right-angled at A and AD is perpendicular to BC. If BD=7\cdot 5\text{ cm} and DC=10\text{ cm}, then what is AD equal to?
- A. 5\text{ cm}
- B. 5\sqrt{2}\text{ cm}
- C. 5\sqrt{3}\text{ cm} ✓
- D. 10\text{ cm}
Correct Answer: C. 5\sqrt{3}\text{ cm}
Explanation
In a right-angled triangle where a perpendicular is dropped from the right angle to the hypotenuse, AD^2 = BD \times DC. Thus, AD^2 = 7.5 \times 10 = 75 \implies AD = \sqrt{75} = 5\sqrt{3}\text{ cm}.
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