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: Identify the scale - factor relationship

The problem states that for every 1 inch of scale - drawing A, scale - drawing B shows a length of 12 inches. The scale factor \(k\) from A to B is the ratio of the lengths in B to the lengths in A. So, \(k = 12\).

Step2: Understand the relationship between scale - factor and area

The relationship between the areas of two similar figures (scale drawings are similar) is given by \(A_{B}=k^{2}A_{A}\), where \(A_{A}\) is the area of the figure in scale - drawing A and \(A_{B}\) is the area of the corresponding figure in scale - drawing B. To find the area of the kitchen in scale - drawing B, first find the area of the kitchen in scale - drawing A (\(A_{A}\)). Then multiply \(A_{A}\) by \(k^{2}=12^{2}=144\) to get the area of the kitchen in scale - drawing B.

Answer:

a. The scale factor relating scale - drawing B to scale - drawing A is 12.
b. First, find the area of the kitchen in scale - drawing A. Then multiply this area by the square of the scale factor (144) to find the area of the kitchen in scale - drawing B.