Question

The sides of a triangle are in the ratio 3:4:5. if its area is 384 cm2, find the sides?

Answer 1

Step-by-step explanation:

Let the sides be 3x , 4x and 5x .

Applying Heron's Formula

$area = \sqrt{s(s - a)(s - b)(s - c)}$

Where ,

$s = \frac{a + b + c}{2}$

$s = \frac{3x + 4x + 5x}{2} = 6x$

$384 = \sqrt{6x(6x - 5x)(6x - 4x)(6x - 3x)}$

$384 = \sqrt{6x(x)(2x)(3x)}$

$384 = \sqrt{36 {x}^{4} }$

$384 = 6 {x}^{2}$

${x}^{2} = 64$

$x = 8$

Therefore the sides are

3x = 3×8 = 24 cm

4x = 4×8 = 32 cm

5x = 5×8 = 40 cm

I hope it helps you. If you have any doubts, then don't hesitate to ask.

Answer 2

Answer:

let the sides of triangle be 3x, 4x, 5x

area of triangle =384 cm2

3x + 4x + 5x = 384

12 x = 384

x = 384/12

x = 32

3x = 3 × 32 = 96

4x = 4 × 32 = 128

5x = 5 × 32 = 160

hence sides of triangle are 96,128,160 cm