Question

If the sides of a triangle are in ratio 5: 4 : 3 then the respective attitudes on them will be in ratio?
A. 3:4:5 B. 5:4:3
C. 20:15:6 D. 12:15:20

Answer 1

Heya!

Here is your answer.

Let the ratio be x

So, the other ratios will be => 5x, 4x and 3x

Let's consider this triangle as a right angled triangle.

Let's name it ∆ ABC

AB and BC are 90° so, AC and BC are the altitude.

AC = 3x
BC = 4x

Area of ∆ ABC =

$\frac{1}{2} \times AC \times BC = \frac{1}{2} \times AB \times CD \\ = > \frac{1}{2} \times 3x \times 4x = \frac{1}{2} \times 5x \times CD \\ = > CD = \frac{1}{2} \times 3x \times 4x \div \frac{1}{2} \times 5x = \frac{12x}{5}$

So, AC : CB : CD = 3x : 4x : 12/15x (multiplying by 5 and dividing by x)

=> 15 : 20 : 12

ANSWER -> 12 : 15 : 20 (d)

Answer 2

Step-by-step explanation:

Heya!

Here is your answer.

Let the ratio be x

So, the other ratios will be => 5x, 4x and 3x

Let's consider this triangle as a right angled triangle.

Let's name it ∆ ABC

AB and BC are 90° so, AC and BC are the altitude.

AC = 3x

BC = 4x

Area of ∆ ABC =

$</p><p>\begin{gathered} \frac{1}{2} \times AC \times BC = \frac{1}{2} \times AB \times CD \\ = > \frac{1}{2} \times 3x \times 4x = \frac{1}{2} \times 5x \times CD \\ = > CD = \frac{1}{2} \times 3x \times 4x \div \frac{1}{2} \times 5x = \frac{12x}{5} \\ \end{gathered} </p><p>$

So, AC : CB : CD = 3x : 4x : 12/15x (multiplying by 5 and dividing by x)

=> 15 : 20 : 12

ANSWER -> 12 : 15 : 20 (d)