How to do math problems in junior high school? From one point to three sides of an equilateral triangle as a vertical line, it is known that the lengths of these three vertical lines are 1.3.5 respectively, and the equilateral three are found. Solution: If A is AM⊥BC, then AM is the height on the side of BC.

Connect PA, PB, PC,

Then the area of △ABC is s =1/2bc * am =1/2 (BC * PD+AB * PF+AC * PE).

∴BC*AM=BC*PD+AB*PF+AC*PE，

∫△ABC is an equilateral triangle,

∴AB=BC=AC，

∴bc*am=bc*pd+bc*pf+bc*pe=bc*(pd+pf+pe)，

∴PD+PE+PF=AM，

∴△ the height of ∴△ABC is: 1+3+5=9,

A=6√3 is obtained by solving the Pythagorean theorem series equation.

By s= 1/2ah=27√3.