Question

the sides of a triangle are in the ratio 12 17 25 and its semi perimeter is 270 cm. find it's area

Answer 1

Answer:

$hope \: its \: helpful \: to \: you$

Answer 2

Ratio of sides of ∆ is 12:17:25.

Semi perimeter of ∆ is 270 cm.

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☯ Let sides of ∆ be 12x, 17x and 25x.

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Here,

Semi - Perimeter of ∆ is 270 cm

Therefore,

Perimeter of ∆ is 2 × 270 = 540 cm

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We know that,

☯ Perimeter of ∆ = sum of all sides

➯ 540 = 12x + 17x + 25x

➯ 540 = 54x

➯ x = 10

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Therefore,

Measure of all sides of ∆ is,

• 12x = 12 × 10 = 120

• 17x = 17 × 10 = 170

• 25x = 25 × 10 = 250

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⋆ Reference of image is shown in diagram

$\setlength{\unitlength}{1cm}\begin{picture}(6,5)\thicklines\put(1,0.5){\line(2,1){3}}\put(4,2){\line(-2,1){2}}\put(2,3){\line(-2,-5){1}}\put(0.7,0.3){ \sf A }\put(4.05,1.9){ \sf B }\put(1.7,2.95){ \sf C }\put(3,2.7){ \sf 120 cm }\put(0.6,1.7){ \sf 170 cm }\put(3,1.07){ \sf 250 cm }\end{picture}$

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We know that,

☯ Area of ∆ is can be find using Heron's Formula,

$\star\;\sf Area = \sqrt{s(s - a)(s - b)(s - c)}$

where,

s = Semi - perimeter

➯ s = 270 cm

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★ Now, Putting values,

$:\implies\sf Area = \sqrt{270(270 - 120)(270 - 170)(270 - 250)}$

$:\implies\sf Area = \sqrt{270(150)(100)(20)}$

$:\implies\sf Area = \sqrt{270 \times 150 \times 20}$

$:\implies{\underline{\boxed{\sf{\pink{9000\;cm^2}}}}}\;\bigstar$

$\therefore$ Area of triangle is 9000 cm².