Since all triangles in these questions are similar, we use that the ratios of corresponding sides are equal
(1)
[tex]\frac{y}{6}[/tex] = [tex]\frac{9}{x}[/tex] = [tex]\frac{5}{4}[/tex]
solving [tex]\frac{9}{x}[/tex] = [tex]\frac{5}{4}[/tex] ( cross-multiply )
5x = 36 ( divide both sides by 5 )
x = [tex]\frac{36}{5}[/tex]
solving [tex]\frac{y}{6}[/tex] = [tex]\frac{5}{4}[/tex]
4y = 30 ⇒ y = [tex]\frac{15}{2}[/tex]
(2)
let h be the height of the flagpole, then
[tex]\frac{h}{5.5}[/tex] = [tex]\frac{50}{4}[/tex]
4h = 275 ⇒ h = 68.75 feet
(3)
[tex]\frac{x}{6}[/tex] = [tex]\frac{93.5}{12.75}[/tex]
12.75x = 561 ⇒ x = 44 feet
