Geometry Problem 1

Geometry Level 3

In triangle $ABC$ , $\angle BAC = 45^\circ$ . $D$ is a point on $BC$ such that $AD$ is perpendicular to $BC$ . If $BD = 3$ and $DC = 2$ , and the area of the triangle $ABC$ is $x$ , find the value of $x$ .

10 12.5 15 20 25 17.5 16

2 solutions

Sergio La Malfa
Jul 16, 2016

LET AD=y x=5y/2

tg BAD=3/y

tg ACB= tg(45°+BAD)=y/2 then

(tg45°+tgBAD)/(1-tg45°tgBAD)=(1+tgBAD)/(1-tgBAD)=(1+3/y)/(1-3/y)= y/2

(y+3)/(y-3)=y/2 then y²-5y-6=0 then y=6 e x=15

Ahmad Saad
May 10, 2016

Geometry Problem 1

2 solutions

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