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40 votes
i need help with this problem a map of a rectangular park has a length of 4 inches and a width of 6 inches.it uses a scale of 1 inch for every 30 miles. what is the length and thw width of the park in real life? show your work and specify which values represent the length and width of the park.

User Ankit Srivastava
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1 Answer

11 votes
11 votes

1) Gathering the data

4 inches x 6 in

Scale 1:30

In real life?

2) Scale are by definition a proportion:

4 inches = 6. 31 x 10^-5 miles

6 inches =9.46 x 10^-5 miles


\begin{gathered} \text{Scale}=\frac{Draw}{\operatorname{Re}al\text{ size}} \\ (1)/(30)=\frac{6.31\cdot10^(-5)\cdot4^{}\cdot10^(-5)}{R} \\ R=1.89\cdot10^{-3\text{ }}and\text{ 1.2}\cdot10^(-3) \end{gathered}

Scale = measure in the Draw/ Real measure

1/30 = 6. 31 x 10^-5 x 9.46 x 10^-5 /R

R= 1.89 . 10^-3 x 1.2 x 10^-3

Multiplying each dimension by 30, we'll get: 0.019 miles and 0.012 miles

So the length is 1.89 . 10^-3 miles and width is 1.2 x 10^-3 miles in real size

User McX
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