Chapter 8.4, Problem 65PFA

To determine

To find: The polynomial that is equivalent to $c^2$

Answer to Problem 65PFA

The polynomial $20x^2+4x+10$ is equivalent to $c^2$

  $C$ is the correct option.

Explanation of Solution

Given:

The legs of the right triangle have lengths of $2x+3$ and $4x-1$ .

Options are

  $\begin{array}{l}\mathrm{A }6x+2\\ \mathrm{B }4x^2+12x+9\\ \mathrm{C }20x^2+4x+10\\ \mathrm{D }36x^2+24x+4\end{array}$

Calculation:

The Pythagoras theorem is given by $a^2+b^2=c^2\mathrm{...}\left(i\right)$

Here, $a=2x+3,b=4x-1$

Substituting these values in the equation $\left(i\right)$

  $\begin{array}{l}{\left(2x+3\right)}^2+{\left(4x-1\right)}^2=c^2\\ c^2=4x^2+12x+9+16x^2-8x+1\\ c^2=20x^2+4x+10\end{array}$

Hence, $C$ is the correct option.