Question

If $a:b:c=13:5:12$, then prove that the triangle is right angled at $A$.

Answer 1

$a:b:c=13:5:12$

Let $x$ be common factor

So ,$a=13xb=5xc=12x$

Checking for pythagoras theorem,

$(13x{)}^2=(5x{)}^2+(12x{)}^{2}169x^2=25x^2+144x^{2}169x^2=169x^2$

So it is right angled at $A$