Question

The ratio of bases of two triangles is x:y and that of their areas is a:b. Then the ratio of their corresponding altitudes wll be
A) ay:bx
B) a:b
C) x:y
D) bx:ay

Answer 1

Answer:   A) ay:bx 


a : b =(1/2 * x * H) : (1/2 * y * h) 

bxH = ayh        => H/h =ay/bx 

Hence H:h = ay:bx

Answer 2

Since , ratios of bases of two triangles is x:y.

And ratio of their areas is a:b.

Using, ar.∆ = 1/2 × b × h.

ar.∆1 : ar.∆2 = (1/2 × b1 × h1) : (1/2 × b2 × h2).

a:b = (x:h1):(y:h2)

$\frac{a}{b} = \frac{xh1}{yh2}$

Cross multiplication,

ayh2 = bxh1

or , bxh1 = ayh2

h1/h2 = ay/ bx

h1 : h2 = ay : bx

Hence , the right option is A.