Two right triangles share a side as follows. What is the area of triangle ACE?
The area of triangle ACE is 30.
For triangle CEA, let height from CA to E be h1
For triangle DEB, let height from DB to E be h2
h1 + h2 = 6, ratio of CA/DB = 8/6 = 4/3 ie h1 = 4/3(h2)
h1 + h2 = 6 => 4/3(h2) + h2 = 7/3h2 = 6 => h2 = 18/7, h1 = 24/7
Area of ACE = (1/2)(8(24/7) = 48/7 sq units