Question

The sides of a triangular plot are in the ratio of 3:5:7 and it's perimeter is 300m. Find the area? ​

Answer 1

Answer:

1500√3 m²

step-by-step explanation:

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Answer 2

Answer:

$1500\sqrt{3} m^{2}$

Step-by-step explanation:

Let the ratio of the sides be 3x:5x:7x.

Since the perimeter is 300m, 3x + 5x + 7x = 300, implies 15x = 300.

Thus, x = 20.

Therefore, the sides are 3x = 3 x 20 = 60m, 5x = 5 x 20 = 100m, and 7x = 7 x 20 = 140m respectively.

Also, s = perimeter/2 = (60 + 100 + 140)/2 = 150m.

Now, by Heron's formula, area = $\sqrt{s(s-a)(s-b)(s-c)}$  

                                                   = $\sqrt{150(150-60)(150-100)(150-140)}$

                                                   = $\sqrt{6750000}$

                                                   = $1500\sqrt{3} m^{2}$

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