Question

The points A (2, 9), B (a, 5) and C (5,5) are the vertices of a triangle ABC right angled at B.

Find the values of a and hence the area of $△ABC$.

Answer 1

AB=
BC=
CA=
Since ABC is a right angled triangle therefore,

or,

or, a(a-5)-2(a-5)=0
or, (a-5)(a-2)=0
∴, either, a-5=0
or, a=5
or, a-2=0
or, a=2
∴, When a=5,
AB=
BC=
which is not possible.
Therefore, a=2
AB=
BC=
Area of the right angled triangle ABC is:

=
=6 sq. unit