Question

Show that:

The ratio of the areas of two triangles of the same height is equal to the ratio of their bases.

Answer 1

Consider  the following figure:

Here AP ⊥ BC

Since Ar. ( ΔABD ) = `1/2` BD x AP

And, Ar. ( ΔADC ) =`1/2` DC x AP

`["Area"( ΔABD)]/["Area"(Δ ADC )] = [1/2 BD xx AP]/[1/2 DC xx AP]= (BD)/(DC)`

Hence proved.