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If the points A (2, 9), B (a, 5) and C (5, 5) are the vertices of a ABC right angled at B, then find the values of a and hence the area of ΔABC.

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If the points A (2, 9), B (a, 5) and C (5, 5) are the vertices of a ABC right angled at B, then find the values of a and hence the area of ΔABC.
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Solution:

Given that, the points A (2, 9), B(a, 5) and C(5, 5) are the vertices of a ΔABC right angled at B.

By Pythagoras theorem, 

AC2 = AB2 +BC2 .....(i)

Hence, the required area of ΔABC is 6 sq units.

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