Question

Show that:
The ratio of the areas of two triangles on the same base is equal to the ratio of their heights.

Answer 1

Consider the following figure :

Here
Ar. ( ΔABC ) = `1/2` BM x AC
and, Ar. ( ΔADC ) = `1/2` DN x AC

`["Area"( Δ"ABD")]/["Area(Δ ADC )"] = [1/2 "BM" xx "AC"]/[1/2 "DN" xx "AC"]= "BM"/"DN"`

hence proved