Chapter 8.1, Problem 44PPS

To determine

The derivation of the Pythagorean Theorem.

Answer to Problem 44PPS

  $a^2+b^2=c^2$

Explanation of Solution

Given:

The given figure is:

  

Calculation:

According to the Pythagorean Theorem, the sum of the longest side of a right triangle is equal to the sum of the squares of the other two sides.

According to the Geometric Mean Leg Theorem,

  $\begin{array}{l}{a}^2=yc\mathrm{...........}\left(1\right)\\ b^2=xc\mathrm{............}\left(2\right)\end{array}$

Adding corresponding sides of the equations 1 and 2,

  $\begin{array}{l}{a}^2+b^2=yc+xc\\ a^2+b^2=\left(y+x\right)c\\ a^2+b^2=\left(c\right)c\\ a^2+b^2=c^2\end{array}$