Chapter 14.4, Problem 4MRE

To determine

To find: Scale factor of $\Delta ODE$ to $\Delta OFG$ .

Answer to Problem 4MRE

Scale factor of $\Delta ODE$ to $\Delta OFG$ is $3:5$ .

Explanation of Solution

Given information :

  $\overline{ED}\left|\right|\overline{BC}\left|\right|\overline{FG}$

Concept used:

If two objects have the same shape, they are called "similar." When two figures are similar, the ratios of the lengths of their corresponding sides are equal. To determine if the triangles shown are similar, compare their corresponding sides.

As per the given problem

Following diagram is provided.

  

Given: $\overline{ED}\left|\right|\overline{BC}\left|\right|\overline{FG}$

  $\Delta ODE$ similar to $\Delta OFG$ .

  $\begin{array}{l}\frac{OD}{OF}=\frac{DE}{FG}=\frac{EO}{GO}\\ \Rightarrow \frac{OD}{OF}=\frac{x}{3+w}=\frac{\frac{9}{2}}{3+\frac{9}{2}}=\frac{9}{6+9}=\frac{9}{15}=\frac{3}{5}\end{array}$

Hence,

: Scale factor of $\Delta ODE$ to $\Delta OFG$ is $3:5$ .