Chapter 12, Problem 11GRFC

To determine

Find the value of b .

Answer to Problem 11GRFC

  $b=\pm 15$

Explanation of Solution

Given:

  $8^2+b^2={17}^2$

Calculation:

  $\begin{array}{l}{8}^2+b^2={17}^2\\ \Rightarrow b^2={17}^2-8^2\mathrm{..............}[subtract{\text{ 8}}^2\text{ from each side]}\\ \Rightarrow b^2=(17+8)(17-8)\mathrm{..}[a^2-b^2=(a+b)(a-b)\\ \Rightarrow b^2=(25)(9)\\ \Rightarrow b=\pm \sqrt{(25)(9)}\mathrm{.......................}[take\text{ square root each side]}\\ \Rightarrow b=\pm 15\end{array}$