Question

Math stuff help please

Answer 1

Card 1)

let's first off, convert the decimal amounts to fractions, and then use proportions of the corresponding sides of each figure.

`\bf \cfrac{BC}{HI}=\cfrac{AB}{GH}\implies \cfrac{5}{HI}=\cfrac{1.5}{4.5}\implies \cfrac{5}{HI}=\cfrac{~~(15)/(10)~~}{(45)/(10)}\implies \cfrac{5}{HI}=\cfrac{~~(3)/(2)~~}{(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}`

Card 2)

we'll change the decimals to fractions as well here, let's check the ratio

`\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{~~(15)/(10)~~}{(25)/(10)}=\cfrac{~~(75)/(10)~~}{x} \\\\\\ \cfrac{~~(3)/(2)~~}{(5)/(2)}=\cfrac{~~(15)/(2)~~}{(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(1)/(2)\implies \boxed{x=12.5}`