Question

three sides of a triangular plot are in the ratio of 3:5:7 and its perimeter is 300m.find its area.

Answer 1

Hey friend,
Here is the answer you were looking for:
$let \: the \: first \: side \: be \: 3x \\ second \: side \: be \: 5x \\ and \: the \: third \: side \: be \: 7x \\ \\ perimeter \: = 300m \: \: \: \: \: (given) \\ \\ a + b + c = 300 \\ \\ 3x + 5x + 7x = 300 \\ \\ 15x = 300 \\ \\ x = \frac{300}{15} \\ \\ x = 20 \\ \\ first \: side \: \\ 3x \\ = 3 \times 20 \\ = 60 \\ \\ second \: side \\ = 5x \\ = 5 \times 20 \\ = 100 \\ \\ third \: side \\ = 7x \\ = 7 \times 20 \\ = 140 \\ \\ semi \: perimeter = \frac{perimeter}{2} \\ \\ s = \frac{300}{2} \\ \\ s = 150m \\ \\ area \: of \: triangle \\ = \sqrt{s(s - a)(s - b)(s - c)} \\ \\ = \sqrt{150(150 - 60)(150 - 100)(150 - 140)} \\ \\ = \sqrt{150(90)(50)(10)} \\ \\ = \sqrt{150 \times 90 \times 50 \times 10} \\ \\ = \sqrt{6750000} \\ \\ = 2598.07 {cm}^{2}$


Hope this helps!!!!

@Mahak24

Thanks...
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