Question

Sides of the triangle are in ratio 12:17:25 ands its perimeter is 540 cm. find its area

Answer 1

Let ratio be x
17x+12x+25x=54x
X=540/54=10
And see in the photo

Answer 2

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$\huge{\underline{\underline{\sf{\blue{SOLUTION:-}}}}}$

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$\sf{\underline{\pink{Answer-}}} </h2><h3>$

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• The area of this triangle is 9000 cm²

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$\sf{\underline{\pink{Given-}}}$

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• Sides of the traingle are ratio = 12:17:25

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• the perimeter of the triangle = 540 cm

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$\sf{\underline{\pink{To \: Find-}}}$

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• The area of the traingle

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$\sf{\underline{\pink{Explanation-}}}$

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• Let the common ratio between the sides of the given triangle be x.

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• Therefore, the side of the triangle will be 12x, 17x, and 25x.

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$\sf{\underline\green{Formula\:Used\:Here-}}$

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$\bigstar\:\boxed{\sf{\red{Heron's \: formula,}}}$

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$\sf{\underline{\pink{Putting\:the\:values:-}}}$

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$\sf\longrightarrow Perimeter \: of \: this \: triangle = 540 cm$

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$\sf\longrightarrow 12x + 17x + 25x = 540 cm$

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$\sf\longrightarrow54x = 540 cm</p><p></p><p>$

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$\sf\longrightarrow x = 10cm$

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• Sides of the triangle will be 120 cm, 170 cm, and 250 cm

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$\sf{\underline{\blue{Now-}}}$

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$\sf \longrightarrow s = \frac{perimeter \: of \: traingle}{2} = \frac{540cm}{2} = 270cm$

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$\sf{\underline{\green{Heron's \: formula,-}}}$

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$\sf \longrightarrow area \: of \: traingle = \sqrt{s(s - a)(s - b)(s - c)}$

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$\sf \longrightarrow \sqrt{270(270 - 120)(270 - 170)(270 - 250) } ^{cm2}$

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$\sf \longrightarrow \sqrt{270 \times 150 \times 100 \times 20} ^{ {cm}^{2} }$

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$\sf \longrightarrow9000 \: {cm}^{2}$

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• Hence,The area of this triangle is 9000 cm²

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