+308 +125 In acute triangle ABC , we know the side lengths AB = sqrt(41) and BC = sqrt(34) and that altitude BD = 5 . What is AC ?
[asy]
size(5cm);
pair A,B,C,D;
A=(0,0);
B=(4,5); <#> D=(4,0); <#> C=(7,0); <#> draw(B--C--A--B--D); <#> draw(rightanglemark(B,D,A)); <#> label("$A$",A,W); <#> label("$B$",B,N); <#> label("$C$",C,E); <#> label("$D$",D,S); <#> label("$\sqrt{41}$",
read more .. +40 +40 +40 Find the area of the triangle below
draw((0,0)--(2sqrt(2),0)--(0,sqrt(2))--cycle);
label("$2r$", (sqrt(2), 0), S);
label("$r$", (0, sqrt(2)/2), W);
label("$\sqrt{10}$", ((2sqrt(2),0)+(0,sqrt(2)))/2, NE);
draw(rightanglemark((0,1),(0,0),(1,0),5)); <#> [/asy]
read more .. +92 +92 +4