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Question-186172




Question Number 186172 by normans last updated on 01/Feb/23
Answered by HeferH last updated on 01/Feb/23
((231)/2) ?  147
$$\cancel{\frac{\mathrm{231}}{\mathrm{2}}\:?} \\ $$$$\mathrm{147}\: \\ $$
Answered by mr W last updated on 01/Feb/23
Commented by mr W last updated on 01/Feb/23
say S=half of the paralellogram  B+36+18+9=S  B+C+18=S  ⇒C=36+9=45 ✓  (D/C)=(9/(18))=(1/2)  ⇒D=(C/2)=((45)/2) ✓  (B/A)=((C+18)/(36))=((63)/(36))=(7/4)  A+C+D=S=B+C+18  A+D=B+18  A+((45)/2)=((7A)/4)+18  ⇒A=6 ✓  ⇒B=((7×6)/4)=((21)/2) ✓  ⇒S=((21)/2)+36+18+9=((147)/2)  ⇒area of paralellogram=2S=147 ✓
$${say}\:{S}={half}\:{of}\:{the}\:{paralellogram} \\ $$$${B}+\mathrm{36}+\mathrm{18}+\mathrm{9}={S} \\ $$$${B}+{C}+\mathrm{18}={S} \\ $$$$\Rightarrow{C}=\mathrm{36}+\mathrm{9}=\mathrm{45}\:\checkmark \\ $$$$\frac{{D}}{{C}}=\frac{\mathrm{9}}{\mathrm{18}}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\Rightarrow{D}=\frac{{C}}{\mathrm{2}}=\frac{\mathrm{45}}{\mathrm{2}}\:\checkmark \\ $$$$\frac{{B}}{{A}}=\frac{{C}+\mathrm{18}}{\mathrm{36}}=\frac{\mathrm{63}}{\mathrm{36}}=\frac{\mathrm{7}}{\mathrm{4}} \\ $$$${A}+{C}+{D}={S}={B}+{C}+\mathrm{18} \\ $$$${A}+{D}={B}+\mathrm{18} \\ $$$${A}+\frac{\mathrm{45}}{\mathrm{2}}=\frac{\mathrm{7}{A}}{\mathrm{4}}+\mathrm{18} \\ $$$$\Rightarrow{A}=\mathrm{6}\:\checkmark \\ $$$$\Rightarrow{B}=\frac{\mathrm{7}×\mathrm{6}}{\mathrm{4}}=\frac{\mathrm{21}}{\mathrm{2}}\:\checkmark \\ $$$$\Rightarrow{S}=\frac{\mathrm{21}}{\mathrm{2}}+\mathrm{36}+\mathrm{18}+\mathrm{9}=\frac{\mathrm{147}}{\mathrm{2}} \\ $$$$\Rightarrow{area}\:{of}\:{paralellogram}=\mathrm{2}{S}=\mathrm{147}\:\checkmark \\ $$

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