Question

the side of a triangular plot are in the are in the ratio of 6.7.8 and it's perimeter is 420m .find the area


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Answer 1

$6x + 7x + 8x = 420 \\ 21x = 420 \\ x = \frac{420}{21} \\ x = 20 \\ a = 120 \: \: b = 140 \: \: c = 160 \\ s = \frac{420}{2} = 210 \\ area \\ = \sqrt{210(210-120)(210-140)(210-160)} \\ = \sqrt{210 \times 9 \times 7 \times 5} \\ = 105 \sqrt{6} \: {cm}^{2}$