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