Chapter 12.1, Problem 46SPR

To determine

To calculate : To find the required scale factor.

Answer to Problem 46SPR

The required scale factor is $\frac{7}{11}$ .

Explanation of Solution

Given information : Consider the given figure with areas:

  

Formula used : The scale factor between green and blue parallelogram can be found by,

  $\frac{\text{Area}\text{of}\text{the}\text{green}\text{parallelogram}}{\text{Area}\text{}\text{of}\text{the}\text{blue}\text{parallelogram}}={\left(\frac{x}{22}\right)}^2$

Calculation : The required scale factor is,

  $\begin{array}{l}\frac{98}{242}={\frac{x}{484}}^2\\ 242x^2=484\cdot 98\\ x^2=\frac{484\cdot 98}{242}\\ x=14\text{m}\end{array}$

Therefore the scale factor is $\frac{14}{22}=\frac{7}{11}$ .