Answer: height=6, width=9 and height=15, width=22.5
Step-by-step explanation:
If the rectangle has a height ([tex]h[/tex]) to width ([tex]w[/tex]) ratio of 3:4.5:
[tex]\frac{h}{w}=\frac{3}{4.5}=0.66[/tex]
We can find other dimensions that fit this relation by multiplying the same number in the numerator as in the denominator.
For example:
If we multiply [tex]\frac{3}{4.5}[/tex] by [tex]\frac{2}{2}[/tex]:
[tex](\frac{3}{4.5})(\frac{2}{2})=\frac{6}{9}=0.66[/tex]
As we can see [tex]\frac{6}{9}[/tex] gives ues the same result as [tex]\frac{3}{4.5}[/tex]
Another example:
If we multiply [tex]\frac{3}{4.5}[/tex] by [tex]\frac{5}{5}[/tex]:
[tex](\frac{3}{4.5})(\frac{5}{5})=\frac{15}{22.5}=0.66[/tex]
As we can see [tex]\frac{15}{22.5}[/tex] gives ues the same result as [tex]\frac{3}{4.5}[/tex]
