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.

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#### 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.

Concept: Properties of Ratios of Areas of Two Triangles

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