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.
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.