Chapter 8.4, Problem 7PSA

To determine

To find the value of two sides.

Answer to Problem 7PSA

The value of AC is 4 and EF is 14.

Explanation of Solution

Given information:

  $\Delta ABC~\Delta DEF$

Formula used:

The below properties are used:

Corresponding sides of similar triangles are proportional.

Means extremes product theorem:

If a product of a pair of not zero numbers is equal to the product of another pair of not zero numbers, then either pair of numbers be made the extremes, and the other pair the means, of proportion.

Calculation:

It is given that,

  $\Delta ABC~\Delta DEF$

  

Corresponding sides of similar triangles are proportional.

  $\begin{array}{l}AB/BC=DE/EF\\ 6/7=12/EF\end{array}$

Applying means extremes product theorem, we get

  $\begin{array}{l}6*EF=84\\ \therefore EF=14\end{array}$

Corresponding sides of similar triangles are proportional.

  $\begin{array}{l}AB/AC=ED/DF\\ 6/AC=12/8\end{array}$

Applying means extremes product theorem, we get

  $\begin{array}{l}12*AC=48\\ \therefore AC=4\end{array}$