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