Question

The side of triangle in ratio
- 3:5:7 and

its
in the ratio
perimeten 300 m. find its area​

Answer 1

Answer:

Let coefficient of ratios be X.

then,

3x+5x+7x=300

15x=300

X=20

Sides of triangle are :-

60 m + 100 m + 140 m

By Heron's formula,

We have,

s = \frac{a + b + c}{2} \\ s = \frac{300}{2} \\ s = 150 \\ area = \sqrt{s(s - a)(s - b)(s - c)} \\ = \sqrt{150(150 - 60)(150 -100)(150 - 140)} \\ = \sqrt{150 \times 90 \times 50 \times 10} \\ = \sqrt{15 \times 9 \times 5 \times 10000} \\ = \sqrt{75 \times {3}^{2} \times {10}^{4} } \\ = \sqrt{75} \times 3 \times {10}^{2} \\ = \sqrt{75} \times 300 \\ = \sqrt{25 \times 3} \times 300 \\ = \sqrt{ {5}^{2} \times 3} \times 300 \\ = 1500 \times \sqrt{3} \\ = 1500 \sqrt{3} {m}^{2}

Answer 2

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Let hthe ratio to the variable x.

Sides = 3x, 5x, 7x

Given,

Perimeter = 300

3x + 5x + 7x = 300

15x = 300

x = 20 m

Sides = 60, 100, 140

So, by herons formula,

s = Perimeter / 2 = 150

Area = √s(s-a) (s-b) (s-c)

Area = √150(150-60)(150-100)(150-140)

Area = √5² * 3* 2 ( 90 ) ( 50) (10)

Area = 5√3 * 2 * (10*3²) ( 5²*2) (10)

Area = 5 * 3* 5* 10* 2 √3

Area = 1500√3 m²

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