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Category: Mensuration

Question-123489

Question Number 123489 by peter frank last updated on 25/Nov/20 Answered by MJS_new last updated on 25/Nov/20 $$\mathrm{gcd}\:\left(\mathrm{54},\:\mathrm{78}\right)\:=\mathrm{6}=\mathrm{side}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{square} \\ $$$$\frac{\mathrm{78}}{\mathrm{6}}×\frac{\mathrm{54}}{\mathrm{6}}=\mathrm{13}×\mathrm{9}=\mathrm{117}=\mathrm{number}\:\mathrm{of}\:\mathrm{squares} \\ $$ Commented by peter…

Question-188901

Question Number 188901 by Mingma last updated on 08/Mar/23 Answered by Frix last updated on 08/Mar/23 $${AB}=\sqrt{\mathrm{8}^{\mathrm{2}} +\left(\mathrm{10}−\mathrm{4}\right)^{\mathrm{2}} }=\mathrm{10} \\ $$$${BC}=\sqrt{\mathrm{8}^{\mathrm{2}} +\mathrm{10}^{\mathrm{2}} }=\mathrm{2}\sqrt{\mathrm{41}} \\ $$$${R}_{{ABC}}…

Question-123302

Question Number 123302 by peter frank last updated on 24/Nov/20 Answered by MJS_new last updated on 24/Nov/20 $${y}={a}\left({x}−\mathrm{2}\right)\left({x}+\mathrm{2}\right)={ax}^{\mathrm{2}} −\mathrm{4}{a} \\ $$$$\mathrm{3}=−\mathrm{3}{a}\:\Rightarrow\:{a}=−\mathrm{1} \\ $$$${y}=\mathrm{4}−{x}^{\mathrm{2}} \\ $$$$\mathrm{the}\:\mathrm{rest}\:\mathrm{is}\:\mathrm{easy}…

Question-123141

Question Number 123141 by ajfour last updated on 23/Nov/20 Commented by ajfour last updated on 23/Nov/20 $${Find}\:{side}\:{length}\:{of}\:{the}\:{congruent} \\ $$$${squares}\:{if}\:{BC}=\mathrm{1}\:{and}\:{AC}\:{such} \\ $$$${that}\:{two}\:{such}\:{congruent}\:{squares} \\ $$$${be}\:{possible}.\:\angle{B}\:=\:\mathrm{90}°. \\ $$…