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Question Number 166715 by alephzero last updated on 26/Feb/22

$$\mathrm{The}\mathrm{perimeter}\mathrm{of}\mathrm{an}\mathrm{equilateral}$$$$\mathrm{triangle}\mathrm{is}24.\mathrm{Find}{\mathrm{it}}^{\prime }\mathrm{s}\mathrm{area}.$$

Answered by Rasheed.Sindhi last updated on 26/Feb/22

$$Leteachofsides:$$$$a=b=c=l$$$$perimeter=3l=24$$$$l=8$$$$\overline{)\begin{array}{c}s=\frac{a+b+c}{2};▴=\sqrt{s(s-a)(s-b)(s-c)}\end{array}}$$$$s=\frac{3l}{2}$$$$▴=\sqrt{\frac{3l}{2}{(\frac{3l}{2}-l)}^3}=\sqrt{\frac{3l}{2}\cdot \frac{l^3}{2^3}}=\frac{l^2}{2^2}\sqrt{3}$$$$=\frac{8^2}{4}\sqrt{3}=16\sqrt{3}$$

Commented by alephzero last updated on 26/Feb/22

$${(\frac{3l}{2}-l)}^3=\frac{l}{2}?$$

Commented by Rasheed.Sindhi last updated on 26/Feb/22

$$Sorryformistake!havecorrected$$$$now.\mathcal{T}hankyou!$$

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