Math, asked by neelufar9463, 10 months ago

The sides of triangle are into ratio 3:5:7 perimeter 300m find its area

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Answered by Aditi2266
1
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Answered by Anonymous
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GiveN :-

  • Sides of triangle are in ratio of 3:5:7

  • Perimeter of triangle is 150 m

To FinD :-

  • Area of the triangle

SolutioN :-

Let, Sides of triangle be 3x, 5x and 7x

\longrightarrow \boxed{ \bf Perimeter \:  of \:  triangle = a + b + c } \\  \\\sf \longrightarrow3x + 5x + 7x = 300 \\  \\\sf \longrightarrow15x = 300 \\  \\\sf \longrightarrow x =  \frac{300}{15} \\  \\ \sf \longrightarrow x = 20

So, Sides are :

3x = 3×20 = 60 m

5x = 5×20 = 100 m

7x = 7×20 = 140 m

Now, Semi-perimeter of the triangle :

:\implies \boxed{\bf s =  \frac{a + b + c}{2} }\\  \\:\implies\sf s =  \frac{60+100+140}{2} \\  \\:\implies\sf s =  \frac{300}{2} \\  \\:\implies\sf s = 150

Area of the triangle :

:\implies\boxed{\bf Area = \sqrt{s(s - a)(s - b)(s - c)}} \\  \\:\implies\sf  \sqrt{150(150- 60)(150- 100)(150 - 140 )} \\  \\:\implies\sf  \sqrt{150 \times 90 \times 50 \times 10} \\  \\:\implies\sf  \sqrt{50\times3 \times 5 \times2 \times 3 \times 3  \times 50 \times  \times 5 \times2 } \\  \\:\implies\sf 50 \times 3 \times 5 \times 2 \times \sqrt{3} \\  \\:\implies\sf 1500 \sqrt{3} \:  {m}^{2}

 \large \therefore  \underline{ \bf \blue{Area \:  of \:  triangle \:  is \:  {1500} \sqrt{3} \: {m}^{2}}}

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