Question

weavers are making a carpet from a scale drawing. the carpet will be 10 ft by 14 ft. every 5 in. on the drawing represents 7 ft of carpet. what are the length and width of the scale drawing?

Explanation:

Step1: Convert feet to inches for real - life dimensions

1 foot = 12 inches. The real - life length of the carpet is 14 ft, so in inches it is \(14\times12 = 168\) inches, and the real - life width is 10 ft, so in inches it is \(10\times12=120\) inches.

Step2: Set up proportion for length

We know that 5 inches on the drawing represents 7 ft in real - life. 7 ft is \(7\times12 = 84\) inches. Let the length of the drawing be \(x\) inches. The proportion is \(\frac{5}{84}=\frac{x}{168}\). Cross - multiply: \(84x = 5\times168\), \(84x=840\), \(x = 10\) inches.

Step3: Set up proportion for width

Let the width of the drawing be \(y\) inches. Using the same scale \(\frac{5}{84}=\frac{y}{120}\). Cross - multiply: \(84y=5\times120\), \(84y = 600\), \(y=\frac{600}{84}=\frac{50}{7}\approx7.14\) inches.

Answer:

Length: 10 inches, Width: \(\frac{50}{7}\approx7.14\) inches