Question

Sides of a triangle are in the ratio of 4 : 6 : 7 and its perimeter is 340 cm. its area is​

Answer 1

Step-by-step explanation:

let the sides of a triangle=x

first side = 4x

second side= 6x

third side= 7x

perimeter=340 cm

perimeter of triangle= sum of all sides

340=4x+6x+7x

340=17x

340/17=x

20=x

put the x=20

first side=4x=4×20=80cm

second side=6x=6×20=120cm

third side=7×20=140cm

Answer 2

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

• Sides of triangle = 4 : 6 : 7
• perimeter = 340cm

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$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

• Area of triangle = ??

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$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

$\sf{\red{\boxed{\bold{Perimeter = A + B + C}}}}$

• Let the sides be 4x , 6x , 7x

$\sf: \implies{\bold{ 4x + 6x + 7x = 340cn}}$

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$\sf: \implies{\bold{ 17x = 340cm}}$

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$\sf: \implies{\bold{ x = \dfrac{340}{17}}}$

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$\sf: \implies{\bold{ x = 20cm}}$

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• Putting the value of X

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4x = 4 × 20cm = 80cm

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6x = 6 × 20cm = 120cm

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7x = 7 × 20cm = 140cm

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$\sf{\red{\boxed{\bold{semi\: perimeter = \dfrac{perimeter}{2}}}}}$

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$\sf: \implies{\bold{ Semi\: perimeter = \dfrac{340}{2}}}$

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$\sf: \implies{\bold{ Semi\: perimeter = 170 cm }}$

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$\sf{\red{\boxed{\bold{area = \sqrt{ s( s - a )( s - b )( s - c )}}}}}$

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$\sf: \implies{\bold{Area = \sqrt{ 170 ( 170 - 80)( 170 -120)( 170- 140)}}}$

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$\sf: \implies{\bold{Area = \sqrt{ 170 \times 90\times 50 \times 30 }}}$

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$\sf: \implies{\bold{Area = \sqrt{ 17\times 10 \times 10 \times 3 \times 3 \times 5 \times 10 \times 10 \times 3}}}$

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$\sf: \implies{\bold{Area = 300\sqrt{ 17\times 15}}}$

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$\sf: \implies{\bold{Area = 300\sqrt{255}cm }}$

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$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

• Area of the square is 300√255 cm