For the given altitudes, CD is the base . . . . the base is the side opposite the vertex to which the altitude is measured
For ∆ABD, the area is (1/2)(AD)(BH) . . . . formula for area of a triangle
For ∆ACD, the area is (1/2)(AD)(CL) . . . . formula for area of a triangle
The ratio of ((1/2)(AD)(BH)) / ((1/2)(AD)(CL)) is 1/2 . . . . given (& substitution property of equality)
The simpified form of this expression is BH/CL = 1/2 . . . . properties of arithmetic
In ratio form, this expression is BH : CL = 1 : 2 . . . . equivalence of ratio expressions
