Question Number 186557 by Mingma last updated on 06/Feb/23
Answered by mr W last updated on 06/Feb/23
$${h}={height}\:{of}\:{trapezoid} \\ $$$${area}\:{of}\:{trapezoid}\:=\frac{\left(\mathrm{5}+\mathrm{6}\right){h}}{\mathrm{2}} \\ $$$${area}\:{of}\:{triangle}\:{with}\:{base}\:{b}=\frac{{bh}}{\mathrm{2}} \\ $$$${which}\:{is}\:{a}\:{third}\:{of}\:{the}\:{total}\:{area}, \\ $$$${therefore} \\ $$$$\frac{{bh}}{\mathrm{2}}=\frac{\mathrm{1}}{\mathrm{3}}×\frac{\left(\mathrm{5}+\mathrm{6}\right){h}}{\mathrm{2}} \\ $$$$\Rightarrow{b}=\frac{\mathrm{5}+\mathrm{6}}{\mathrm{3}}=\frac{\mathrm{11}}{\mathrm{3}} \\ $$$${a}=\mathrm{5}−{b}=\mathrm{5}−\frac{\mathrm{11}}{\mathrm{3}}=\frac{\mathrm{4}}{\mathrm{3}} \\ $$$$\Rightarrow\frac{{a}}{{b}}=\frac{\mathrm{4}}{\mathrm{11}}\:\checkmark \\ $$