The required co-ordinates of the triangle are as follows: (3,4), (5,2), (a, 5) Therefore we can find the area bounded by the triangle using determinant method. Hence
ΔArea=
1
2
(
1
3
4
1
5
2
1
a
5
)=
1
2
(
1
1
1
3
5
a
4
2
5
) =
1
2
[(25−2a)−(15−4a)+(6−20)]
=
1
2
[(25−15−14)−2a+4a] =
1
2
[−4+2a] Now it is given that the area of the triangle so formed is 3 sq. units. Hence 3=
1
2
|2a−4| |2a−4|=6 2a−4=±6 2a=10,2a=−2 a=5,a=−1 Therefore,one of the values of 'a' is 5