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Question
The ratio of the areas of two triangles with the common base is 14 : 9. Height of the larger triangle is 7 cm, then find the corresponding height of the smaller triangle.
Solution
Let the height of the larger triangle be h1 and that of the smaller triangle be h2.
The ratio of the areas of two triangles with a common base is equal to the ratio of their corresponding heights.
`"Area(larger Triangle)"/"Area(smaller Triangle)"="h"_1/"h"_2`
`14/9=7/"h"_2`
`14xx "h"_2=9xx7`
`therefore"h"_2=(9xx7)/14=9/2`
`therefore"h"_2=4.5" cm"`
The corresponding height of the smaller triangle is 4.5 cm.
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