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

## Triangle Area

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- hitesh1983
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I think this question is a case of superfluous information.hitesh1983 wrote: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

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.

Shalabh Jain,

e-GMAT Instructor

e-GMAT Instructor