ABC is a triangle right angled at B. P is the midpoint of AB and Q is the mid-point of BC. Consider the following: I. AQ = \sqrt{73} units II. CP = \sqrt{52} units Which of the above is/are required to determine the area of the triangle?

Explanation

Let AB = c and BC = a. Using Pythagoras theorem, AQ^2 = c^2 + (\frac{a}{2})^2 = 73 and CP^2 = (\frac{c}{2})^2 + a^2 = 52. These give two linear equations in terms of a^2 and c^2. Solving them simultaneously provides the values of a and c, which are needed to calculate the area \frac{1}{2}ac. Hence, both statements are required.

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