Question

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

Answer 1

Let the heights of the two triangles are 3x and 4x
Let the bases of the two triangles are p and q respectively.
We know that, area of the triangle = $\frac{1}{2}$ ×base×height
 Ratio of areas = 4 : 3
$\frac{1}{2}$ × p ×3x : $\frac{1}{2}$ × q × 4x = 4 : 3

3px : 4qx = 4 : 3

Product of extremes = product of means

9px = 16qx

p/q = 16/ 9

p : q = 16 : 9

Answer 2

Let the bases of the two triangles be x and y and their heights be 3h and 4h respectively.Then,((1/2) X x X 3h)/(1/2) X y X 4h)
 =4/3 =x/y =(4/3 X 4/3)=16/9

Required ratio = 16 : 9.