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Category: Geometry

Question-218890

Question Number 218890 by Spillover last updated on 17/Apr/25 Answered by mr W last updated on 17/Apr/25 $$\frac{\mathrm{1}}{\mathrm{1}}×\frac{{BF}}{{FD}}×\frac{\mathrm{3}}{\mathrm{4}}=\mathrm{1}\:\Rightarrow\frac{{BF}}{{FD}}=\frac{\mathrm{4}}{\mathrm{3}} \\ $$$$\Rightarrow\Delta_{{ADF}} =\frac{\mathrm{3}}{\mathrm{7}}×\Delta_{{ADB}} =\frac{\mathrm{3}}{\mathrm{7}}×\frac{\mathrm{3}×\mathrm{3}}{\mathrm{2}}=\frac{\mathrm{27}}{\mathrm{14}} \\ $$$$\left[{CDFE}\right]=\Delta_{{ACF}} −\Delta_{{ADF}}…

Question-218844

Question Number 218844 by Spillover last updated on 16/Apr/25 Answered by som(math1967) last updated on 16/Apr/25 $${let}\:{lenth}\:{of}\:{rectangle}={l},{width}={b} \\ $$$$\:\mathrm{2}{l}+\mathrm{6}{b}=\mathrm{4}{l}+\mathrm{2}{b}={side}\:{of}\:{square} \\ $$$$\Rightarrow\mathrm{4}{b}=\mathrm{2}{l}\Rightarrow{l}=\mathrm{2}{b} \\ $$$$\:{l}×{b}=\mathrm{18}\Rightarrow\mathrm{2}{b}^{\mathrm{2}} =\mathrm{18}\Rightarrow{b}=\mathrm{3},{l}=\mathrm{6} \\…