Triangle Area

[hitesh1983]

Perimeter of triangle is 12, One side 5 other side 3
height perpendicular to third side is 3, need to find the area

Please help in solving
I was able to solve it using Hero's formula but was n't sure if thats the correct approach

[hitesh1983]

Please ignore i am able to solve it

[Shalabh's Quants]

Perimeter of triangle is 12, One side 5 other side 3
height perpendicular to third side is 3, need to find the area

Please help in solving
I was able to solve it using Hero's formula but was n't sure if thats the correct approach

I think this question is a case of superfluous information.

There is no need of either perimeter data or height data to calculate area.

Soln.--If Ht. not given..

Perimeter is 12, hence 3rd side= 12-5-3=4;

Now, since semi-perimeter s= Perimeter/2=12/2=6.

=> So, Area=sqrt{(s(s-a)(s-b)(s-c)}; Hero's Formula.

=> Area=sqrt{6.1.3.2)=6.

Soln.--If Perimeter is not given..

Say 3rd side=a;

Then, Area=1/2.ht.3rd side=1/2.3.a=3a/2 ----------(1)

Now, since semi-perimeter s= Sum of all sides/2

=> s=(5+3+a)/2=(8+a)/2;

So, Area=sqrt{(s(s-a)(s-b)(s-c)}-----------(2)

equate eqn.1 & 2.

=> 3a/2=sqrt{(s(s-a)(s-b)(s-c)}

=> 3a/2=sqrt{((8+a)/2((8+a)/2-a)((8+a)/2-5)((8+a)/2-3)}

There is no need to solve this equation. Better approach is plug in value from Answer choice & see if LHS & RHS are equal.