Question 212484
The area of a triangle is 12. That is all that is given and I want to know what are the side lengths and angles.


Step 1.  To make this problem easier, let's assume a right triangle.


Step 2.   Area of Triangle A is 


{{{A=bh/2}}}



where b=base and h=height or b and h are also the legs of the right triangle.


Step 3.   Area= A = 12.  So let b=4 and solve for h.


{{{A=bh/2}}}


{{{12=4h/2}}}


{{{12=2h}}}


Divide by 2 from both sides of equation


{{{12/2=2h/2}}}


{{{6=h}}}


Using Pythagean Theorem, hypotenuse c ia



{{{c=sqrt(4^2+6^2)}}}


{{{c=sqrt(20)}}}


Step 4.  Sides  4, 6 and {{{sqrt(20)}}}.  With the b=4 and h=6 and the Area A={{{(4*6)/2=12}}}



Hope the steps were helpful.  Good luck in your studies.  

 
Respectfully, 
Dr J


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