Answer:
45 feet
Step-by-step explanation:
Given
[tex]Scale: \frac{1}{2}in \ to \ 5ft[/tex]
[tex]Scale\ Length =4\frac{1}{2}\ in[/tex]
Required
Determine the actual length
First, we need to represent the scale as a ratio:
[tex]\frac{1}{2}\ in: 5\ ft[/tex]
Next, we represent the scale length and actual length as another ratio:
[tex]4\frac{1}{2}\ in: x[/tex]
Where x represent the actual measurement when [tex]Scale\ Length =4\frac{1}{2}\ in[/tex]
Equate both ratios:
[tex]\frac{1}{2}\ in: 5\ ft = 4\frac{1}{2}\ in: x[/tex]
Convert to fractions
[tex]\frac{1}{2}/5 = 4\frac{1}{2}/x[/tex]
Convert to improper fraction
[tex]\frac{1}{2}/5 = \frac{9}{2}/x[/tex]
[tex]\frac{1}{2} * \frac{1}{5} = \frac{9}{2} * \frac{1}{x}[/tex]
[tex]\frac{1}{10} = \frac{9}{2x}[/tex]
Cross Multiply
[tex]2x * 1 = 9 * 10[/tex]
[tex]2x = 90[/tex]
Divide through by 2
[tex]x = 45[/tex]
