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The Ratio of the Areas of Two Triangles with Common Base is 6:5. Height of the Larger Triangle of 9 Cm, Then Find the Corresponding Height of the Smaller Triangle. - Geometry

The ratio of the areas of two triangles with common base is 6:5. Height of the larger triangle of 9 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 `h_2`

The ratio of the areas of two triangles with common base is equal to the ratio of their corresponding heights.

`(A("Larger"triangle))/(A("Smaller"triangle)) = h_1/h_2`

`:. 6/5 = 9/h_2`  ...(Substituting the given values)

`∴ 6 xx h_2 = 9 xx 5`

`:. h_2 = (9 xx 5)/6 = 15/2`

`:. h_2= 7.5 cm`

The corresponding height of the smaller traingles of 7.5 cm.

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