In triangle EFG, tan∠GEF = 22/7, and the altitude from E divides FG into segments of length 3 and 17.

Determine the area of triangle EFG.

Denote the height to base FG by h, hits the base at the point K.

**S=10*h**

22/7=TAN(FEK+GEK)=( 3/h+17/h)/(1-51/(h^2))

The positive root of the quadratic equation

**11h^2-70h-561=0**

turns to be **h=11**

**so the area is 110** (square units)

Rem: a high school textbook problem