Question

a walk in the park
some friends plan to visit new york city and want to walk the perimeter of
central park, the most visited urban park in the united states.
how many miles will they walk?
the map is a scale drawing of
central park.
you can use a table of equivalent ratios to determine the actual length
and width of central park based on the scale of the drawing.
the scale is 1 in. = 0.5 mi.

step 1 use the table to identify the length and width of the park.

a map length of 5 inches is equivalent to a park length of 2.5 miles.
a map length of 1 inch is equivalent to a park length of 0.5 mile.

step 2 use the formula ( p = 2 ( ell + w ) ) to find the perimeter.

( p = 2 ( ell + w ) )
( p = 2 ( 0.5 + 2.5 ) )
( p = 2 ( 3 ) ) or 6
the friends will walk 6 miles if they walk the perimeter of central park.
lets explore more
a. how could you use the information you found to find the area of central park?

Explanation:

Step1: Recall the formula for the area of a rectangle

The formula for the area of a rectangle is \(A = l\times w\), where \(l\) is the length and \(w\) is the width.

Step2: Identify the length and width of Central Park

From the previous problem, we know that the length \(l = 2.5\) miles and the width \(w=0.5\) miles.

Step3: Substitute the values into the area formula

Substitute \(l = 2.5\) and \(w = 0.5\) into \(A=l\times w\). So, \(A=2.5\times0.5\).

Step4: Calculate the product

\(2.5\times0.5=\frac{25}{10}\times\frac{5}{10}=\frac{125}{100} = 1.25\)

Answer:

We use the formula for the area of a rectangle \(A = l\times w\). Substitute the length \(l = 2.5\) miles and width \(w = 0.5\) miles (found from the scale - table relationship) into the formula. The area of Central Park is \(1.25\) square miles.