Question

the original scale factor for a scale drawing of a house plan is 1/80, and the length of the original scale drawing is 12 inches. what is the length in inches of the new scale drawing if the scale factor of the new scale drawing to actual length of the house is 1/160?

Explanation:

Step1: Find actual length from original scale

Given original scale factor is $\frac{1}{80}$, and length on original scale - drawing is 12 inches. Let actual length be $L$. Using the scale - factor formula $\text{Scale factor}=\frac{\text{Length on scale - drawing}}{\text{Actual length}}$, we have $\frac{1}{80}=\frac{12}{L}$, so $L = 12\times80=960$ inches.

Step2: Find length on new scale - drawing

The new scale factor is $\frac{1}{160}$. Let the length on new scale - drawing be $l$. Again using the scale - factor formula $\frac{1}{160}=\frac{l}{960}$. Cross - multiply: $l=\frac{960}{160}=6$ inches.

Answer:

6 inches