Question

The sides of a triangle are in the ratio of 3:5: 7. If the perimeter of
the triangle is 60 cm, then its area is
[
a) 603 sq.cm. b) 30/3 sq.cm c) 15 3 sq.cm d) 1203 sq.cm
:​

Answer 1

$\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}$

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$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

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

• Perimeter of the triangle is 60 cm

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$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

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• Area of the triangle

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$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

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Given that the sides of a triangle are in the ratio of 3:5:7

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So,

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Let the sides be 3x , 5x , 7x

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Also given that the perimeter is 60 cm

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So,

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➜ 3x + 5x + 7x = 60

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➜ 15x = 60

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➜ x = 4

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So the sides are -

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• 3x = 3(4) = 12 cm

• 5x = 5(4) = 20 cm

• 7x = 7(4) = 28 cm

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$\underline{\bold{\texttt{Area of triangle :}}}$

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➠ $\sf \sqrt { s(s - a)(s - b)(s - c) }$ ⚊⚊⚊⚊ ⓵

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Where ,

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• a = 1st Side

• b = 2nd Side

• c = 3rd Side

• s = Semi Perimeter

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• s = $\sf \dfrac { a + b + c } { 2 }$

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$\underline{\bold{\texttt{Area of given triangle :}}}$

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• a = 12

• b = 20

• c = 28

• s = $\sf \dfrac { 12 + 20 + 28 } { 2 }$

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$\sf s = \dfrac { 60 } { 2 }$

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• s = 30

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⟮ Putting the above values in ⓵ ⟯

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➜ $\sf \sqrt { s(s - a)(s - b)(s - c) }$

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➜ $\sf \sqrt { 30(30 - 12)(30 - 20)(30 - 28) }$

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➜ $\sf \sqrt { 30(18)(10)(2) }$

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➜ $\sf \sqrt { 300(36) }$

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➜ $\sf 6 \sqrt { 2 \times 2 \times 3 \times 5 \times 5 }$

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➜ $\sf 6 \times 2 \times 5 \sqrt 3$

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➜ $\sf 60 \sqrt 3$

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➜ 103.9

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➨ 104 sq. cm. approx

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Hence the area of given triangle is 104 sq. cm.