# 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. - Geometry

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.

Concept: Properties of Ratios of Areas of Two Triangles
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