Proof based on Triangles

Question

for an acute triangle,prove that $a^2+b^2>c^2$
Well, I dropped a perpendicular from B to O but still I can't prove the question because I can't prove that $2a^2>2cz$

Where z is the side BO Pls help me

For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to. — Martin R, Mar 03 '22 at 15:07
Ohkay, but in the class they haven't taught cosine rule yet, though I know that, but guess the teacher wants us to prove with geometry — Death Champion, Mar 03 '22 at 15:16

score 1 · Accepted Answer · answered Mar 03 '22 at 15:31

1

Assuming angle B to be an acute angle.

Let $BL=x$,

Thus $AL^2=c^2-x^2=b^2-(a-x)^2 \implies c^2+a^2-b^2=2ax\implies c^2+a^2\geq b^2 $( as $2ax \geq 0$ )

answered Mar 03 '22 at 15:31

Proof based on Triangles

1 Answers1