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Category: Mensuration

Question-187701

Question Number 187701 by Mingma last updated on 20/Feb/23 Answered by HeferH last updated on 20/Feb/23 $${let}\:“{h}''\:{be}\:{the}\:{height}\:{of}\:{the}\:{top}\:{triangle}\:{and}\:“{a}'' \\ $$$${the}\:{base} \\ $$$$\:\frac{\mathrm{7}{ah}}{\mathrm{2}}\:=\:\mathrm{28} \\ $$$$\:{ah}\:=\:\frac{\mathrm{28}\centerdot\mathrm{2}}{\mathrm{7}}\:=\:\mathrm{8}\: \\ $$$$\:{Total}\:{area}\:=\:\mathrm{4}{a}\centerdot\mathrm{4}{h}\centerdot\frac{\mathrm{1}}{\mathrm{2}}\:=\:\mathrm{8}{ah}\:=\:\mathrm{64}{u}^{\mathrm{2}}…

Question-121793

Question Number 121793 by ajfour last updated on 11/Nov/20 Commented by ajfour last updated on 13/Nov/20 $${If}\:{O}\overset{\frown} {{DE}}\:\:\:{is}\:{a}\:{sector},\:{and}\:\bigtriangleup{ABC}\: \\ $$$${is}\:{equilateral}\:{with}\:{minimum}\:{area} \\ $$$${has}\:{an}\:{area}\:{equal}\:{to}\:\bigtriangleup{OEF}\:,\:{find}\:\theta. \\ $$$$ \\…

Question-187301

Question Number 187301 by Rupesh123 last updated on 15/Feb/23 Answered by HeferH last updated on 16/Feb/23 $$\:{chord}\:{theorem}: \\ $$$$\mathrm{5}^{\mathrm{2}} \:=\:{x}\left(\mathrm{5}\:+\:\mathrm{3}\right) \\ $$$$\:\frac{\mathrm{25}}{\mathrm{8}}\:=\:{x} \\ $$$$\:\frac{\mathrm{25}}{\mathrm{8}}\:+\:\mathrm{8}\:=\:\mathrm{2}{r} \\…

Question-187253

Question Number 187253 by Rupesh123 last updated on 15/Feb/23 Answered by MikeH last updated on 15/Feb/23 $$\left(\mathrm{i}\right)\:\mathrm{Area}\:\mathrm{of}\:\bigtriangleup{BCD}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{4}\right)\left(\mathrm{4}\right)\:\mathrm{sin}\:{x}\:=\:\mathrm{8}\:\mathrm{sin}\:{x} \\ $$$$\:\:\:\:\:\:\:\mathrm{Area}\:\mathrm{of}\:\Delta{ABD}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{3}\right)\left(\mathrm{4}\right)\mathrm{sin}\:\left(\mathrm{90}−{x}\right)\:=\:\mathrm{6}\:\mathrm{cos}\:{x} \\ $$$$\mathrm{total}\:\mathrm{area}\:=\:\mathrm{area}\:\mathrm{of}\:\Delta{BCD}\:+\:\mathrm{area}\:\mathrm{of}\:\Delta{ABD} \\ $$$$\Rightarrow\:{A}\:=\:\mathrm{6}\:\mathrm{cos}\:{x}\:+\:\mathrm{8}\:\mathrm{sin}\:{x}\:\blacksquare \\ $$…