ABC is a triangle right-angled at B. If AC = \frac{(p+q)}{2} and BC = \frac{(p-q)}{2}, then which of the following statements is/are correct ? I. The value of AB is equal to the geometric mean of p and q. II. The perimeter of the triangle is p(q+1). Select the answer using the code given below :
- A. I only ✓
- B. II only
- C. Both I and II
- D. Neither I nor II
Correct Answer: A. I only
Explanation
Using Pythagoras theorem, AB^2 = AC^2 - BC^2 = (\frac{p+q}{2})^2 - (\frac{p-q}{2})^2 = pq. Thus, AB = \sqrt{pq}, which is the geometric mean of p and q (I is true). Perimeter = AB + BC + AC = \sqrt{pq} + p, which does not equal p(q+1) (II is false).
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