Question

Please answer fast and correct. If u r not sure pls write that not sure. If u will write I will mark u brainist

Answer 1

Given: Three sides of a triangle are 5 m, 6 m and 7 m respectively.

To find: Area of triangle?

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$\underline{\bigstar\:\boldsymbol{Using\: Heron's\:Formula\::}}$

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

$:\implies\sf s = semi - perimeter$

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

$\sf Here \begin{cases} & \sf{a = \bf{5\:m}} \\ & \sf{b = \bf{6\:m}} \\ & \sf{c = \bf{7\:m}} \end{cases}$

$:\implies\sf s = \dfrac{5 + 6 + 7}{2}$

$:\implies\sf s = \cancel{\dfrac{18}{2}}$

$:\implies{\underline{\boxed{\frak{\purple{s = 9\:m}}}}}\;\bigstar$

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$\bf{\dag}\;{\underline{\frak{Now,\:Putting\:values\;in\;formula}}}$

$:\implies\sf Area_{\;\triangle} = \sqrt{9(9 - 5)(9 - 6)(9 - 7)}$

$:\implies\sf Area_{\;\triangle} = \sqrt{9 \times 4 \times 3 \times 2}$

$:\implies\sf Area_{\;\triangle} = 3 \times 2 \sqrt{3 \times 2}$

$:\implies{\underline{\boxed{\frak{\purple{Area_{\;\triangle} = 6\sqrt{6}\:m^2}}}}}\;\bigstar$

$\therefore\:{\underline{\sf{Area\:of\:triangle\:is\: \bf{6 \sqrt{6}\:cm^2}.}}}$

Answer 2

Aɴsᴡᴇʀ :

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❍ $\rm \bf{Option (b),}$$\boxed{\tt{\red{6\sqrt{6}\: m^{2}}}}$

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Gɪᴠᴇɴ :

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$\begin{gathered} ❍ \:\rm \bf Sides \begin{cases} & \rm{a = {5\:m}} \\ & \rm{b = {6\:m}} \\ & \rm{c = {7\:m}} \end{cases} \\\end{gathered}$

Tᴏ Fɪɴᴅ :

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❍ Area of the triangle (∆).

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Fᴏʀᴍᴜʟᴀ :

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❍ $\boxed{\sf{\green{∆=\sqrt{s(s-a)(s-b)(s-c)}}}}$

Where, $\sf \bf {\:s = \dfrac{a+b+c}{2}}$

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Sᴏʟᴜᴛɪᴏɴ :

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

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➪ $\sf{\purple{s = \dfrac{5+6+7}{2}}}$

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➪ $\sf{\purple{s = \dfrac{18}{2} = 9m}}$

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➪ $\sf{\red{∆=\sqrt{s(s-a)(s-b)(s-c)}}}$

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➪ $\sf{\red{∆=\sqrt{9(9-5)(9-6)(9-7)}}}$

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➪ $\sf{\red{∆=\sqrt{9(4)(3)(2)}}}$

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➪ $\sf{\red{∆=\sqrt{36\times 6}}}$

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➪ $\sf{\red{∆=}}$${\bf{\red{6\sqrt{6} \:m^2}}}$