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Category: Geometry

Question-222958

Question Number 222958 by mr W last updated on 11/Jul/25 Commented by mr W last updated on 12/Jul/25 $${find}\:{the}\:{area}\:{of}\:{the}\:{smallest}\: \\ $$$${inscribed}\:{equilateral}\:{triangle}\:{of}\:{a} \\ $$$${given}\:{triangle}\:{with}\:{sides}\:{of}\:{lengthes} \\ $$$$\mathrm{3},\:\mathrm{5},\:\mathrm{7}\:{respectively}.…

Question-222830

Question Number 222830 by Tawa11 last updated on 08/Jul/25 Answered by Frix last updated on 08/Jul/25 $$\underset{{i}=\mathrm{1}} {\overset{{k}} {\sum}}…= \\ $$$$=\frac{\mathrm{32}}{\mathrm{9}}\underset{{i}=\mathrm{1}} {\overset{{k}} {\sum}}\frac{{i}^{\mathrm{3}} }{{k}^{\mathrm{4}} }+\mathrm{120}\underset{{i}=\mathrm{1}}…

Question-222753

Question Number 222753 by mr W last updated on 06/Jul/25 Answered by A5T last updated on 07/Jul/25 $$\mathrm{Let}\:\theta\:\mathrm{be}\:\mathrm{the}\:\mathrm{base}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{any}\:\mathrm{of}\:\mathrm{the}\:\mathrm{isosceles}\:\bigtriangleup \\ $$$$\mathrm{180}−\mathrm{2}\theta+\mathrm{180}−\left(\mathrm{2}\left(\mathrm{180}−\theta−?\right)\right)+\mathrm{90}=\mathrm{180} \\ $$$$\Rightarrow\mathrm{2}?=\mathrm{90}\Rightarrow?=\mathrm{45}° \\ $$ Commented…