Respuesta :
A poster that is 18 inches long is similar to another that is 45 inches long (and 30 inches wide). The scale factor that is used to reduce the size of the painting is shown as;
(a) Scale factor = 18/45
Scale factor = 2/5
This is because the scale of reduction means multiplying the original size by a value that makes it reduce to a smaller size. Hence the scale factor calculated shows that the painting is reduced by a factor of 5 inches to 2 inches, hence its 2/5.
(b) The width of the poster is 18 inches long can be derived by multiplying the width of the painting by the scale factor and that is;
[tex]\begin{gathered} \text{Scale factor=}\frac{2}{5} \\ \frac{45}{30}=\frac{18}{x} \\ \text{Cross multiply;} \\ 45x=18(30) \\ x=\frac{18(30)}{45} \\ x=12 \end{gathered}[/tex]The width of the poster that is 18 inches long is 12 inches wide
(c) All posters are sized using the same scale of 2/5.
A second poster is 16 inches long and 14 inches wide.
That means the dimensions of the actual painting are as follows;
[tex]\begin{gathered} \text{Length;} \\ \frac{16}{x}=\frac{2}{5} \\ 2x=5(16) \\ x=\frac{80}{2} \\ x=40 \\ \text{Width;} \\ \frac{14}{y}=\frac{2}{5} \\ 2y=5(14) \\ y=\frac{70}{2} \\ y=35 \end{gathered}[/tex]Therefore, for another poster that is 16 inches long and 14 inches wide, the dimensions of the actual painting are
Length = 40 inches
Width = 35 inches
