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

Answer:

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}

2

1

×base×height

Ratio of areas = 4 : 3

\frac{1}{2}

2

1

× p ×3x : \frac{1}{2}

2

1

× 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

Answer:

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}

2

1

×base×height

Ratio of areas = 4 : 3

$\implies\frac{1}{2}$

2

1

× p ×3x : \frac{1}{2} 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