Question

find area of triangle 39m,52m,65m by herons formula​........???​

Answer 1

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

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

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• 1st side of triangle is 39 m

• 2nd side of triangle is 52 m

• 3rd side of triangle is 65 m

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

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• Area of triangle

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

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By Heron's formula

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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

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

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For the given triangle

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• a = 39 m

• b = 52 m

• c = 65 m

• $\sf s = \dfrac { 39 + 52 + 65} { 2 }$

• $\sf s = \dfrac { 156} { 2 }$

• s = 78

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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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➜ $\sf \sqrt { 78(78 - 39)(78 - 52)(78 - 65) }$

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➜ $\sf \sqrt { 78(39)(26)(13) }$

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➜ $\sf \sqrt {1028196 }$

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➨ 1014 sq. m.

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• Hence the area of triangle is 1014 sq. m.

Answer 2

$\Large{\underbrace{\sf{\purple{Required\:Solution:}}}}$

Given thαt,

• Sides of α triαngle αre 39m,52m αnd 65m.

◾️We hαve to find the αreα of the triαngle by using heron's formulαe.

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Heron's Formulαe —

$\large\star{\boxed{\sf{\purple{Area_{(triangle)} = \sqrt{s(s-a)(s-b)(s-c)}}}}}$

Where, s = semiperimeter αnd a,b αnd c = sides.

$\large{\boxed{\sf{ Semiperimeter = \dfrac{a+b+c}{2}}}}$

• Substitute the vαlues αnd simplify.

:$\implies{\sf{ \dfrac{39+52+65}{2}}}$

:$\implies{\sf{\dfrac{156}{2}}}$

:$\implies{\sf{ 78m}}$

• Substitute the vαlues in the heron's formulαe αnd simplify.

:$\implies{\sf{ \sqrt{78(78-39)(78-52)(78-65)}}}$

:$\implies{\sf{ \sqrt{78(39)(26)(13)}}}$

:$\implies{\sf{ \sqrt{1,028,126}}}$

:$\large\implies{\boxed{\sf{\purple{ 1014m^{2}}}}}$

Hence, the αreα of the triαngle us 1014m².

And we αre done! :D

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