An isosceles triangle has sides A, B, and C, such that sides A and B have the same length. Side C has a length of $12$ and the triangle has an area of $81$ . What are the lengths of sides A and B?

Question

1494 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-24T22:32:51

I found $14.77$

Consider the diagram:
enter image source here
The Area is given as:

$"Area"=("Base"xx"Height")/2(CxxH)/2=81$

So:

$(12*H)/2=81$
$H=81/6=13.5$

We use half triangle and Pythagoras:

$A^2=H^2+(C/2)^2=H^2+C^2/4=13.5^2+12^2/4=182.25+36=218.25$

and:

$A=sqrt(218.25)=14.77=B$

An isosceles triangle has sides A, B, and C, such that sides A and B have the same length. Side C has a length of 12 12 and the triangle has an area of 81 81 . What are the lengths of sides A and B?