Card 1)
let's first off, convert the decimal amounts to fractions, and then use proportions of the corresponding sides of each figure.
[tex]\bf \cfrac{BC}{HI}=\cfrac{AB}{GH}\implies \cfrac{5}{HI}=\cfrac{1.5}{4.5}\implies \cfrac{5}{HI}=\cfrac{~~\frac{15}{10}~~}{\frac{45}{10}}\implies \cfrac{5}{HI}=\cfrac{~~\frac{3}{2}~~}{\frac{9}{2}} \\\\\\ \cfrac{5}{HI}=\cfrac{3}{2}\cdot \cfrac{2}{9}\implies \cfrac{5}{HI}=\cfrac{3}{9}\implies \cfrac{5}{HI}=\cfrac{1}{3}\implies \boxed{15=HI}[/tex]
Card 2)
we'll change the decimals to fractions as well here, let's check the ratio
[tex]\bf \cfrac{model}{actual}\qquad \stackrel{cm}{1.5}~~:~~\stackrel{ft}{2.5}\qquad \cfrac{1.5}{2.5}\qquad \qquad \cfrac{1.5}{2.5}=\cfrac{7.5}{x}\implies \cfrac{~~\frac{15}{10}~~}{\frac{25}{10}}=\cfrac{~~\frac{75}{10}~~}{x} \\\\\\ \cfrac{~~\frac{3}{2}~~}{\frac{5}{2}}=\cfrac{~~\frac{15}{2}~~}{\frac{x}{1}}\implies \cfrac{3}{2}\cdot \cfrac{2}{5}=\cfrac{15}{2}\cdot \cfrac{1}{x}\implies \cfrac{3}{5}=\cfrac{15}{2x}\implies 6x=75 \\\\\\ x=\cfrac{75}{6}\implies x=\cfrac{25}{2}\implies x=12\frac{1}{2}\implies \boxed{x=12.5}[/tex]
