Let CH ==y
Let AH ==x
Let CB ==z
x^2 + y^2=18^2...................(1)
15^2 + y^2==z^2.................(2)
z^2 + 18^2=(15 + x)^2.. ....(3), solve for x, y, z
x ==12, y==6*sqrt(5), z=9*sqrt(5)
Area of ABC==1/2 * (12+15) * 6*sqrt(5)==181.1215 u^2
+40 what?!? the question never tooks about the angles and the altitude of a right triangle where the altitude goes through the right angle does not always suggest that it forms a 30-60-90 triangle. Think about it. @Guest is right here.
