+195 In isosceles right triangle $ABC$, shown here, $AC=BC$. Point $X$ is on side $BC$ such that $CX=6$ and $XB=12$, and $Y$ is on side $AB$ such that $\overline{XY}\perp\overline{AB}$. What is the ratio of the area of triangle $BXY$ to the area of triangle $ABC$?
+129849 Note that triangle BYX is similar to triangle BCA
AC = BC = 12 + 6 = 18
BA = sqrt (18^2 + 18^2) = sqrt (2 *18^2) = 18 sqrt (2)
Scale factor of BYX to BCA = 12/ (18 sqrt (2)) = 2/ (3 sqrt (2)) = sqrt (2) / 3
Ratio of area of BYX to BCA = (scale factor)^2 = 2/9
Just as QM found !!!!
You are absolutely right !!! [BXY]/[ABC] = 36/162 = 2/9
