Question

The perimeter of a triangular field is 420m and its sides are in the ratio 6:7:8. Find the area of the triangular field

Answer 1

Given, perimeter of a triangular field is 420 m and its sides are in the ratio 6:7:8.
Let sides of a triangular field be a = 6x, b = 7x and c = 8x.
Perimeter of a triangular field, 2s = a + b + c ⇒ 420 = 6x + 7x + 8x ⇒ 420 = 21x
⇒ x = 420/21 = 20 m.

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Answer 2

Answer:

The area of the triangular field  $2100\sqrt{15}$ sq mts.

Step-by-step explanation:

Heron's Formula:

•  Area of a triangle with length of sides a, b, c and where s is half the perimeter is given by $\sqrt{s(s-a)(s-b)(s-c)}$

Given ratio of sides of a triangular field are 6:7:8

 and also the perimeter of the triangular field = 420mts

  Let the sides be

       a = 6x, b = 7x, c = 8x

   Perimeter of triangular field = 6x+7x+8x = 21x

     According to the given data

      21x = 420

          x = 420/21

          x = 20

  Now substitute the value of x = 20 in 6x, 7x and 8x

   we get the sides of the triangular field as

     a = 6(20) = 120

     b = 7(20) = 140

     c = 8(20) = 160

  By Heron's formula

Area of triangle with sides a, b, c is $\sqrt{s(s-a)(s-b)(s-c)}$

      where s is half the perimeter

            s = (a+b+c)/2

               = (120+140+160)/2

               = 420/2

            s  = 210 m

        Area of the triangular field = $\sqrt{210(210-120)(210-140)(210-160)}$

                                                     = $\sqrt{210(90)(70)(50)}$

                                                     = $2100\sqrt{15}$ sq mts.

    Hence  Area of the triangular field = $2100\sqrt{15}$ sq mts.

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