Chapter 6, Problem 9STP

(a)

To determine

To calculate:Tofind the scaling factor from $\Delta XYZ$ to $\Delta RST$

Answer to Problem 9STP

The scaling factor from $\Delta XYZ$ to $\Delta RST$ is $\frac{2}{3}$

Explanation of Solution

Given information:Similar triangles

Calculation:

Given similar triangles as follows:

Since triangles are similar, hence the corresponding sides of triangles are proportional

Thus, scaling factoring is

$Scale=\frac{XY}{RS}$

On substituting the values,

$\begin{array}{l}Scale=\frac{4}{6}\\ Scale=\frac{2}{3}\end{array}$

Hence, scaling factor is $\frac{2}{3}$

(b)

To determine

To calculate: To find the value of $x$ in $\Delta XYZ$

Answer to Problem 9STP

The value of $x$ in $\Delta XYZ$ is $9.34in.$

Explanation of Solution

Given information: Similar triangles

Calculation:

Given similar triangles as follows:

Since triangles are similar, hence the corresponding sides of triangles are proportional

Thus, scaling factoring is

$\frac{XY}{RS}=\frac{YZ}{ST}$

On substituting the values,

$\frac{4}{6}=\frac{x}{14}$

On solving the above proportion,

$\begin{array}{l}4\times 14=x\times 6\\ x\times 6=4\times 14\\ x=\frac{4\times 14}{6}\\ x=\frac{2\times 14}{3}\\ x=\frac{28}{3}\\ x=9.34\end{array}$

Hence, value of $x$ in $\Delta XYZ$ is $9.34in.$