Chapter 12.1, Problem 44SPR

To determine

To calculate : To find the required scale factor.

Answer to Problem 44SPR

The required scale factor is $\frac{5}{6}$ .

Explanation of Solution

Given information : Consider the given figure with areas:

  

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

  $\frac{\text{Area}\text{of}\text{the}\text{green}\text{trapezoid}}{\text{Area}\text{}\text{of}\text{the}\text{blue}\text{trapezoid}}={\left(\frac{x}{12}\right)}^2$

Calculation : The required scale factor is,

  $\begin{array}{l}\frac{25}{36}={\left(\frac{x}{12}\right)}^2\\ \frac{25}{36}=\frac{x^2}{144}\\ x^2=\frac{25\cdot 144}{36}\\ x=\frac{5\cdot 12}{6}\\ =10\text{cm}\end{array}$

Therefore the scale factor is $\frac{10}{12}=\frac{5}{6}$ .