Chapter 12, Problem 12GRFC

To determine

Find the value of a .

Answer to Problem 12GRFC

  $a=\pm \sqrt{111}$

Explanation of Solution

Given:

  $a^2+6^2={\left(7\sqrt{3}\right)}^2$

Calculation:

  $\begin{array}{l}{a}^2+6^2={\left(7\sqrt{3}\right)}^2\\ \Rightarrow a^2={\left(7\sqrt{3}\right)}^2-6^2\mathrm{..................}[subtract{\text{ 6}}^2\text{ from each side]}\\ \Rightarrow a^2=147-36\\ \Rightarrow a^2=111\\ \Rightarrow a=\pm \sqrt{111}\mathrm{.............................}[\text{take square root each side]}\end{array}$