Question

a city council plans to put a new fence around a local community park. consider the scale drawing of the perimeter of the community park.
if each 2 cm on the scale drawing equals 12.5 feet, what is the actual perimeter, in feet, of the community park?
feet

Explanation:

Step1: Calculate the perimeter of the scale drawing

The perimeter \(P_{scale}\) of a triangle is the sum of its side lengths.
\(P_{scale}=40 + 40+30=110\space cm\)

Step2: Use the scale factor to find the actual perimeter

Given that \(2\space cm\) on the scale drawing equals \(12.5\space feet\). Let the actual perimeter be \(P_{actual}\).
We set up a proportion: \(\frac{2\space cm}{12.5\space feet}=\frac{110\space cm}{P_{actual}}\)
Cross - multiply: \(2\times P_{actual}=110\times12.5\)
\(P_{actual}=\frac{110\times12.5}{2}\)
First, calculate \(110\times12.5 = 1375\)
Then, \(P_{actual}=\frac{1375}{2}=687.5\space feet\)

Answer:

\(687.5\)