Chapter 7, Problem 17PT

To determine

To find: The each measures of $WZ,UZ$ .

Answer to Problem 17PT

The length of the side is $UZ=43.83$ , $WZ=46.83$ .

Explanation of Solution

Given information: The given information is:

  

Calculation:

Consider the figure as shown below:

  

Observing the above figure, the length of the altitude $WU$ is same found by using any of the triangles.

Use Pythagorean Theorem to get the value of the altitude.

  ${\left(x+4\right)}^2-{\left(x+1\right)}^2={\left(36\right)}^2-{\left(32\right)}^2$

Simplify,

  $\begin{array}{l}{\left(x+4\right)}^2-{\left(x+1\right)}^2={\left(36\right)}^2-{\left(32\right)}^2\\ x^2+8x+16-x^2-2x-1=272\\ 6x+15=272\end{array}$

  $\begin{array}{l}6x=257\\ x=\frac{257}{6}\end{array}$

The length of the side $WZ$

  $\begin{array}{l}WZ=x+4\\ WZ=\frac{257}{6}+4\\ WZ=\frac{281}{6}\end{array}$

  $WZ=46.83$

Therefore, the length of the side is $WZ=46.83$ .

  $\begin{array}{l}UZ=x+1\\ UZ=\frac{257}{6}+1\\ UZ=\frac{263}{6}\end{array}$

  $UZ=43.83$

Therefore, the length of the side is $UZ=43.83$ .