Question

What is the ratio of the heights of two triangles which have equal base side and of which the areas are in the ratio 9:16?

Answer 1

height are also in 9:16 form

Answer 2

Let the bases be b and the heights be h1 and h2 and the area be 9x and 16x
The area of triangle 1 = 9x
or, (1/2)*h1*b = 9x.......................1
The area of triangle 2 = 16x
or, (1/2)*h2*b =16x.....................2
Dividing 1 by 2 we get,
[(1/2)*h1*b]/[(1/2)*h2*b] = 9x/16x
or, h1:h2 = 9:16