Question

find the area of following triangle whose side are 60, 153 CM, 111 CM​

Answer 1

Step-by-step explanation:

• a =60
• b =153
• c =111

then (s) = a+b+c/2

(s) =(60+153+111)/2

(s) =324/2=162

$by \: heron \: formula \: \\ \\ area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)} \\ \\ = \sqrt{162(162 - 60)(162 - 153)(162 - 111)} \\ = \sqrt{162 \times 102 \times 9 \times 51 } \\ = 3 \times 17 \times 3 \times 2 \times 9 \\ = 81 \times 34 = 2754cm$

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Answer 2

${\large{ \underline{\underline{ \: \maltese{\orange{\sf{ \: Given \: :- \: }}}}}}}$

$\begin{gathered} \\ \end{gathered}$

• $ide = 60 cm, 153 cm and 111 cm.

$\begin{gathered} \\ \end{gathered}$

${\large{ \underline{\underline{ \: \maltese{\red{\sf{ \: To\:Find\: :- \: }}}}}}}$

$\begin{gathered} \\ \end{gathered}$

• Area = ?

$\begin{gathered} \\ \end{gathered}$

${\large{\underline{\underline{ \maltese{\pmb{\color{blue}{\sf{ \: SolutioN \: : - \: }}}}}}}}$

$\begin{gathered} \\ \end{gathered}$

$\begin{gathered} \\ {\dag \: {\underline{\sf{ \: Calculating\:the \: Semi\:perimeter \: ; \: }}}}\\ \\ \end{gathered}$

$\begin{gathered} \\{\qquad{\quad{ \normalsize{\longmapsto{\sf{s=\dfrac{a+b+c}{2}}}}}}}\\ \\ \end{gathered}$

$\begin{gathered} \\{\qquad{\quad{\normalsize{\longmapsto{\sf{s=\dfrac{60+153+111}{2}}}}}}}\\ \\ \end{gathered}$

$\begin{gathered} \\{\qquad{\quad{\normalsize{\longmapsto{\sf{s \: =\dfrac{324}{2}}}}}}}\\ \\ \end{gathered}$

$\begin{gathered} \\{\qquad{\quad{\normalsize{\longmapsto{\sf{s=\cancel\dfrac{324}{2}}}}}}}\\ \\ \end{gathered}$

$\begin{gathered} \\{\qquad{\quad{\normalsize{\longmapsto{\sf{s=162}}}}}}\\ \\ \end{gathered}$

$\begin{gathered} \\{\qquad{\quad{\normalsize{\therefore{\underline{\boxed{ \color{purple}{\pmb{\sf{ \: Semi\:perimeter\:of\:triangle\:is\:162\:cm}}}}}}}}}}\\ \\ \end{gathered}$

━─━─━─━─━─━─━─━─━─━─━─━─━━─━─━──━─━─━─━━─━─━─

$\begin{gathered} \\{\dag \: {\underline{\sf{ \: Calculating\:the \: Area \: ; \: }}}}\\ \\ \end{gathered}$

$\begin{gathered} \\{\qquad{\quad{\normalsize{\longmapsto{\sf{Area{\:triangle}=\sqrt{s(s-a)(s-b)(s-c)}}}}}}}\\ \\ \end{gathered}$

$\begin{gathered} \\{\qquad{\quad{\normalsize{\longmapsto{\sf{Area=\sqrt{162(162-60)(162-153)(162-111)}}}}}}}\\ \\ \end{gathered}$

$\begin{gathered} \\{\qquad{\quad{\normalsize{\longmapsto{\sf{Area=\sqrt{162(102)(9)(51)}}}}}}}\\ \\ \end{gathered}$

$\begin{gathered} \\{\qquad{\quad{\normalsize{\longmapsto{\sf{Area=\sqrt{7584516}=2754}}}}}}\\ \\ \end{gathered}$

$\begin{gathered} \\{\qquad{\quad{\normalsize{\therefore{\underline{\boxed{ \pmb{\sf{\purple{Area\:of\:triangle\:is\:2754cm^2}}}}}}}}}}\\ \\ \end{gathered}$

━─━─━─━─━─━─━─━─━─━─━─━─━━─━─━──━─━─━─━━─━─━─

$\begin{gathered} \\ \end{gathered}$

$\qquad{\quad{\therefore}}$ Area of given triangle is $\bf{2754\:cm^2.}$

$\begin{gathered}\begin{gathered} \\ {\underline{\rule{280pt}{3pt}}}\\ \\ \end{gathered}\end{gathered}$

❒ Formula Used ::

${\begin{gathered} \\ \dashrightarrow {\boxed{ \bf{s=\dfrac{a+b+c}{2}}}} \bigstar \\ \\ \end{gathered}$

$\begin{gathered} \\ \dashrightarrow {\boxed{\bf{Area=\sqrt{s(s-a)(s-b)(s-c)}}}\bigstar \\ \end{gathered}$

$\begin{gathered}\begin{gathered} \\ {\underline{\rule{280pt}{7pt}}} \end{gathered}\end{gathered}$