Chapter 7, Problem 12CT

To determine

To find: The value of the SU from the given triangle.

Answer to Problem 12CT

The value of the SU is 39

Explanation of Solution

Given information:

  

  $\text{If }PR=14,RS=7,\text{and}RT=26$

Consider two triangles, PRT and $PSU$ . as shown as in the textbook.

  $\overline{RT}\parallel \overline{SU}$

Therefore, corresponding angles are congruent,

  $\begin{array}{l}\angle R\cong \angle S\\ \angle T\cong \angle U\end{array}$

AA Similarity Postulate: if two angles of one triangle are congruent to two angles of another

triangle, then the triangles are similar.

Therefore,

  $\text{Δ}PSU-\text{Δ}PRT$

Now, use property of proportion,

  $\frac{PS}{PR}=\frac{SU}{RT}=\frac{PU}{PT}$

Or, $\frac{PS}{PR}=\frac{SU}{RT}$

As the point R lie on the line PS, thus,

  $PS=PR+RS$

Or, $\frac{PR+RS}{PR}=\frac{SU}{RT}\dots \dots$ (1)

The lengths of the sides are given;

  $\begin{array}{l}SU=?,RS=7\\ RT=26,PR=14\end{array}$

Put the values in the equation (1),

  $\begin{array}{cc}\frac{14+7}{14}& =\frac{SU}{26}\\ 14SU& =546\\ SU& =\frac{546}{14}\\ & =39\end{array}$

Hence, the value of the SU is 39.