Question

In two triangles, the ratio of their areas is 4:3 and that of their heights is 3:4. Find the ratio of their bases ​

Answer 1

Let the heights of two triangles be 3x and 4x

Let the bases of two triangles be p and q respectively

Area of triangle = 1/2 × base × height

ratio of their areas = 4:3

1/2 × p × 3x : 1/2 × q × 4x = 4:3

3px:4qx = 4:3

Products of extremes = product of means

9px= 16qx

p/q = 16/9

p:q = 16:9

Answer 2

Answer:

16:9

Step-by-step explanation:

Let the bases of the two triangles be x and y and their heights be 3h and 4h respectively.

Then, 12×x×3h12×y×4h=43⇒xy=43×43=169

Required ratio = 16 : 9.