Question

the side af a traingular plot are in ratio 2:3:4 and its peri meter is 900m find its area​

Answer 1

Let the common ratio be 2x, 3x, 4x

$2x + 3x + 4x = 900m$

$9x = 900m$

$x = 900 \div 9$

$x = 100$

2x = 2 × 100 = 200m

3x = 3 × 100 = 300m

4x = 4 × 100 = 400m

semiperimeter = a + b + c / 2

200 + 300 + 400 / 2

900 / 2

semiperimeter = 450

Area,

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

$\sqrt{450(450 - 200) \: (450 - 300) \: (450 - 400)}$

$\sqrt{450 \times 250 \times 150 \times 50}$

Then take out the LCM of 450, 250, 150, 50.

$\sqrt{2 \times 3 \times 3 \times 5 \times 5 \times 2 \times 5 \times 5 \times 5 \times 2 \times 3 \times 5 \times 5 \times 2 \times 5 \times 5}$

$2 \times 2 \times 3 \times 5 \times 5 \times 5 \times 5 \sqrt{3}$

= $7500 \sqrt{3} \: {m}^{2}$