Scale Drawing Fencing Word Problem

🔑 Key Concepts

• A scale drawing uses a constant relationship between drawing measurements and real-world measurements.
• The scale in this problem is \(3\) inches represents \(17\) feet.
• To find the fencing needed, first find the perimeter of the yard in the scale drawing.
• The side touching the house does not need fencing, so only the exposed yard boundary is counted.
• A proportion can convert the drawing measurement in inches to the real measurement in feet.

✏️ Worked Examples

Problem from the video: Frank plans to purchase fencing to enclose his backyard. Every \(3\) inches represents \(17\) feet. How many feet of fencing does Frank need?

Step 1: Find the Fence Length on the Drawing

Only count the outside edges of the yard that need fencing.

Top side: \(14\) inches

Left slanted side: \(9\) inches

Right slanted side: \(9\) inches

Bottom exposed parts: \(5+5=10\) inches

\(14+9+9+5+5=42\)

The scale drawing shows \(42\) inches of fencing.

Step 2: Convert Inches to Feet

The scale is \(3\) inches represents \(17\) feet.

Set up a proportion:

\(\frac{3}{17}=\frac{42}{x}\)

Cross multiply:

\(3x=17\cdot42\)

\(3x=714\)

\(\frac{3x}{3}=\frac{714}{3}\)

\(x=238\)

Frank needs \(238\) feet of fencing.

Why This Works

The drawing and the real yard are proportional. Since every \(3\) inches represents \(17\) feet, the total fence length in the drawing can be scaled up using the same ratio.

🧠 Math Vocabulary

• Scale Drawing: A drawing that represents a real object using proportional measurements.
• Scale: The relationship between a measurement on a drawing and the actual measurement.
• Scale Factor: A multiplier used to enlarge or reduce measurements proportionally.
• Proportion: An equation showing that two ratios are equal.
• Ratio: A comparison of two quantities.
• Perimeter: The distance around the outside of a figure.
• Cross Multiply: A method for solving proportions by multiplying diagonally across equal ratios.

💡 Main Idea

A scale drawing can be used to solve real-world measurement problems when the drawing and actual object are proportional. In this problem, students first find the perimeter that needs fencing on the drawing, then use the scale \(3\) inches to \(17\) feet to convert the drawing length into the actual amount of fencing.

📚 What You Should Already Know

Students should know how to find perimeter, add side lengths, read a scale, write equivalent ratios, and solve proportions using multiplication and division.

🚀 What Comes Next

After solving scale drawing word problems, students can apply scale factors to similar figures, maps, blueprints, perimeter, and area problems.

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