Question

The sides of a triangular field are in the ratio of 2:3:4. If its perimeter is 900m, what is the area of the field?

Answer 1

Answer:

100

Step-by-step explanation:

2+3+4=9

900÷9=100

Answer 2

Answer:

$\boxed{\sf Area\:of\:the\:field\:is\:13,50,000\:m^2}$

Step-by-step explanation:

Let the sides of the triangular field be 2x, 3x and 4x.

★ As we know, the sum of sides of a triangle is 180. So :

→ 2x + 3x + 4x = 180

= 9x = 180

= x = 180/9

= x = 20

★ Sides will be :

1. 2x = 2(20) = 40
2. 3x = 3(20) = 60
3. 4x = 4(20) = 80

★ According To The Question :

$\boxed{\rm Area\:of\:triangle = \sqrt{s(s-a) (s-b) (s-c)}}$

→ Sides = 40 + 60 + 80/2 = 180/2 = 90

★ Area :

$= \sqrt{90(90 - 40)(90 - 60)(90 - 80)} \\ = \sqrt{90 \times 50 \times 30 \times 10} \\ = 1350000 \: {m}^{2}$

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