Given : Washington Middle School's school flag has a height: width ratio of 12:27 . (1)
i) Height of school flag = 32 inches
Let x be the width, then ratio of height to width=[tex]\dfrac{32}{x}[/tex]
From (1), we have
[tex]\dfrac{32}{x}=\dfrac{12}{27}\\\\ x=\dfrac{27\times32}{12}=72[/tex]
Hence, If the school flag is 32 inches high then width = 72 inches.
ii) Width of school flag = 48 inches
Let h be the height , then ratio of height to width=[tex]\dfrac{h}{48}[/tex]
From (1), we have
[tex]\dfrac{h}{48}=\dfrac{12}{27}\\\\ x=\dfrac{12\times48}{27}=21.3333333333\approx21.3[/tex]
Hence, If the school flag is 48 inches wide, then height = 21.3 inches.
