Question

scale drawings a and b are made from the same original drawing. scale drawing a is given here. for every 1 inch in scale drawing a, scale drawing b (not shown) shows a length of 12 inches. a. what scale factor relates scale drawing b to scale drawing a? b. describe how the scale factor is used to determine the area of the kitchen in scale drawing b.

Explanation:

Step1: Determine the scale factor

The scale factor is the ratio of the length in scale drawing B to the length in scale drawing A. Given that for every 1 inch in scale drawing A, scale drawing B shows a length of 12 inches. So the scale factor \(k=\frac{\text{Length in B}}{\text{Length in A}}=\frac{12}{1} = 12\).

Step2: Use the scale - factor to find the area

The area of a rectangle is \(A = l\times w\). If the scale factor for lengths is \(k\), the scale factor for areas is \(k^{2}\). First, find the area of the kitchen in scale drawing A. The length of the kitchen in scale drawing A is 1 inch and the width is \(\frac{3}{4}\) inch. So the area of the kitchen in scale drawing A, \(A_{A}=1\times\frac{3}{4}=\frac{3}{4}\) square inches. Then, since the scale factor for areas is \(k^{2}=(12)^{2}=144\), the area of the kitchen in scale drawing B, \(A_{B}=A_{A}\times k^{2}\).

Answer:

a. The scale factor is \(12\).
b. First, find the area of the kitchen in scale drawing A (\(A_{A}=l\times w\), where \(l = 1\) inch and \(w=\frac{3}{4}\) inch). Then, since the scale factor for areas is \(k^{2}\) (where \(k = 12\) is the scale factor for lengths), the area of the kitchen in scale drawing B is \(A_{B}=A_{A}\times k^{2}\).