Math Problem Statement

A scale drawing of a rectangular park had a scale of 1 cm = 60 m. The dimensions of the rectangular park in the drawing are 11.6 cm by 5.9 cm. What is the actual perimeter of the park in meters?

Solution

To solve the problem, we are given the following information:

  • The scale of the drawing is 1cm=60m1 \, \text{cm} = 60 \, \text{m}.
  • The dimensions of the rectangular park in the drawing are 11.6cm11.6 \, \text{cm} by 5.9cm5.9 \, \text{cm}.

Step 1: Convert the drawing dimensions to actual dimensions.

Using the given scale, we multiply the drawing dimensions by 60 to convert them into meters.

  • Actual length = 11.6cm×60=696m11.6 \, \text{cm} \times 60 = 696 \, \text{m}
  • Actual width = 5.9cm×60=354m5.9 \, \text{cm} \times 60 = 354 \, \text{m}

Step 2: Calculate the perimeter of the park.

The perimeter PP of a rectangle is given by the formula:

P=2×(length+width)P = 2 \times (\text{length} + \text{width})

Substituting the actual length and width:

P=2×(696m+354m)=2×1050m=2100mP = 2 \times (696 \, \text{m} + 354 \, \text{m}) = 2 \times 1050 \, \text{m} = 2100 \, \text{m}

Final Answer:

The actual perimeter of the park is 2100m2100 \, \text{m}.

Would you like more details or have any questions?

Here are five related questions:

  1. How would the perimeter change if the scale was 1 cm = 100 m instead?
  2. What would be the area of the park in square meters?
  3. If the park had a walking path along the perimeter, how many laps would make 5 km?
  4. What is the relationship between the drawing’s dimensions and the actual dimensions?
  5. How would the problem change if the park had different shapes?

Tip: When working with scale drawings, always ensure to adjust both dimensions before performing any calculations involving perimeter or area.

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Math Problem Analysis

Mathematical Concepts

Scale conversion
Perimeter of a rectangle

Formulas

Perimeter of a rectangle: P = 2 × (length + width)
Scale conversion: Actual length/width = Drawing length/width × scale factor

Theorems

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Suitable Grade Level

Grades 6-8