Question

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

Answer 1

HEY USER HERE IS UR ANS
let the sides be 6x , 7x, 8x,
Then
Sum=420
6x+7x+8x=420
21x=420
Therefore x= 20
Now
sides =120,140,160
U can now find area using Heron's formula

Answer 2

$\huge\mathfrak{Answer}$

Your Question is like this

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

Ans: Let the side be 6x, 7x and 8x respectively.

Perimeter = 6x + 7x + 8x

=> 420 = 21x

=> x = 420/21

=> x = 20

Sides are,

a = 6x = 6 × 20 = 120 m

b = 7x = 7 × 20 = 140 m

c = 8x = 8 × 20 = 160 m

$s \: = \frac{a + b + c}{2} = \frac{420}{2} = 210m$

Area of $\triangle$

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

$= \sqrt{210(210 - 210)(210 - 140)(210 - 160)}$

$\sqrt{210 \times 90 \times 70 \times 50}$

$\sqrt{21 \times 9 \times 5 \times 7 \times 10 \times 10 \times 10 \times 10}$

$3 \times 10 \times 10\sqrt{(3 \times 7) \times 7 \times 5}$

$300 \times 7 \sqrt{15} = 2100 \sqrt{15} {m}^{2}$

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