Chapter 12.4, Problem 2MRE

To determine

To find : The value of w.

Answer to Problem 2MRE

The value of w is 10.

Explanation of Solution

Given information :

Draw an altitude from point B and use the Pythagorean theorem.

Calculation :

Draw an altitude BE from B to E on the side AD.

In right triangle AEB.

  $\begin{array}{l}AE=AD-ED\\ AE=12-4\\ AE=8\end{array}$ and

  $BE=CD=6$

Now, by Pythagoras Theorem

  $\begin{array}{l}A{B}^2=A{E}^2+B{E}^2\\ w^2=8^2+6^2\\ w^2=64+36\\ w^2=100\\ w=10\end{array}$

Hence,

The value of w is 10.