Chapter 5, Problem 16CUR

To determine

To Find: The numerical length of each side of triangle $SUN$ such that $\angle S\cong \angle N,SU\cong 2x+7$ , $UN=4x-1\text{ and S}N=3x+4$ .

Answer to Problem 16CUR

  $\text{S}N=16,UN=15\text{ and }SU=15$

Explanation of Solution

Given:

In a triangle SUN, $\angle S\cong \angle N,SU\cong 2x+7$ , $UN=4x-1\text{ and S}N=3x+4$ .

Calculation:

In triangle if two angles are equal the sides opposite to these angles are equal.

Since, $\angle S\cong \angle N$ .

Therefore, $SU=UN$ .

  $\begin{array}{l}SU=UN\\ 2x+7=4x-1\\ 2x-4x=-1-7\\ -2x=-8\\ x=4\end{array}$

Substituting $x=4$ in $\text{S}N=3x+4$ .

  $\begin{array}{l}\text{S}N=3x+4\\ \text{S}N=3\times 4+4\\ \text{S}N=16\end{array}$

Substituting $x=4$ in $UN=4x-1$ .

  $\begin{array}{l}UN=4x-1\\ UN=4\times 4-1\\ UN=15\end{array}$

Substituting $x=4$ in $SU\cong 2x+7$ .

  $\begin{array}{l}SU=2x+7\\ SU=2\times 4+7\\ SU=15\end{array}$

Therefore, the answer is $\text{S}N=16,UN=15\text{ and }SU=15$ .